How many questions from Electromagnetic Induction appear in JEE?

Electromagnetic Induction has appeared in 120 of the last 186 JEE Main and JEE Advanced papers — about 65% of them — contributing 155 questions in total across those papers.

Is Electromagnetic Induction an important chapter for JEE?

Judged by how often it is actually tested, it appears in roughly 65% of papers. Chapters above about 50% are effectively guaranteed to show up every session, so they repay thorough preparation; lower-frequency chapters are better treated as targeted revision.

Where do these Electromagnetic Induction questions come from?

Every question is from an official JEE Main or JEE Advanced paper, transcribed from the original paper and tagged to this chapter. Answers follow the official answer key.

Electromagnetic Induction JEE Previous Year Questions with Answers

Q1·PhysicsSingle correctJEE Advanced 2026

List-I contains four conducting loops lying in the

XY

plane, as shown in the figures. The loops are rotating about

Z

axis passing through the point

O

with time period

T

in clockwise direction. The region

x > 0

contains a uniform magnetic field

B

in the

+z

direction. List-II contains the qualitative variation of the induced current

i(t)

for each of these loops. Choose the option which describes the correct match between the entries in List-I to those in List-II.

(A)P → 5, Q → 4, R → 1, S → 3
(B)P → 3, Q → 2, R → 5, S → 4
(C)P → 3, Q → 2, R → 1, S → 4
(D)P → 5, Q → 1, R → 2, S → 3

Q2·PhysicsSingle correctJEE Advanced 2026

Consider a circuit consisting of a capacitor of capacitance

C

and a coil with

N

turns per unit length, cross sectional area

S

and length

d

, where

d^2 \gg S

. There is another coil of length

d/2

, cross sectional area

S/2

and

2N

turns per unit length completely inside the larger coil, as shown in the figure. The ends of this smaller coil are connected with each other by an insulated conducting wire. The self-inductance of the larger coil is

L

. Neglecting edge effects and all the Ohmic resistances, the resonant frequency of the circuit is:

(A) $\frac{4}{\sqrt{15\,LC}}$
(B) $\frac{6}{\sqrt{5\,LC}}$
(C) $\frac{2}{\sqrt{3\,LC}}$
(D) $\sqrt{\frac{2}{3\,LC}}$

Q3·PhysicsSingle correctJEE Main 2026

A 30 cm long solenoid has 10 turns per cm and area of 5 cm

^2

. The current through the solenoid coil varies from 2 A to 4 A in 3.14 s. The e.m.f. induced in the coil is

\alpha \times 10^{-5}

V. The value of

\alpha

is ________.

(A)60
(B)12
(C)120
(D)34

Q4·PhysicsSingle correctJEE Main 2026

An inductor of inductance 10 mH having resistance of 100 Ω is connected to battery of E.M.F. 1.0 V through a switch as shown in the figure below. After switch is closed, the ratio of instantaneous voltages across the inductor when the current passing through it is 2 mA and 4 mA is _______.

(A)4/3
(B)3/4
(C)5/3
(D)3/5

Q5·PhysicsSingle correctJEE Main 2026

A square loop of side 2 cm is placed in a time varying magnetic field with magnitude as

B = 0.4\sin(300t)

Tesla. The normal to the plane of loop makes an angle of 60° with the field. The maximum induced emf produced in the loop is __________ mV.

(A)12
(B)18
(C)21
(D)24

Q6·PhysicsNumericalJEE Main 2026

In the given circuit below inductance values of

L_1

,

L_2

and

L_3

are same. The magnetic energy stored in the entire circuit is

(U_t)

and that stored in the

L_2

inductor is

(U_l)

.

U_t/U_l

is _____. (Ignore the mutual inductance if any)

Q7·PhysicsSingle correctJEE Main 2026

A metal rod of length L rotates about one end at origin with a uniform angular velocity ω. The magnetic field radially falls off as B(r) = B₀e

^{-\lambda r}

; λ being a positive constant. The emf induced (neglecting the centripetal force on electrons in the rod) is :

(A) $B_{0}\omega\left[\dfrac{1}{\lambda^{2}} - e^{-\lambda L}\left(\dfrac{1}{\lambda^{2}} + \dfrac{L}{\lambda}\right)\right]$
(B) $B_{0}\omega\left[\dfrac{1}{\lambda^{2}} + e^{-\lambda L}\left(\dfrac{1}{\lambda^{2}} + \dfrac{L}{\lambda}\right)\right]$
(C) $B_{0}\omega\left[\dfrac{4}{\lambda^{2}} - e^{-2\lambda L}\left(\dfrac{1}{\lambda^{2}} + \dfrac{2L}{\lambda}\right)\right]$
(D) $B_{0}\omega\left[\dfrac{3}{\lambda^{2}} - e^{-3\lambda L}\left(\dfrac{3}{\lambda^{2}} + \dfrac{L}{\lambda}\right)\right]$

Q8·PhysicsNumericalJEE Main 2026

A circular loop of radius 20 cm and resistance 2 Ω is placed in a time varying magnetic field

\vec{B} = (2t^2 + 2t + 3)

T. At

t = 0

, for the plane of the loop being perpendicular to the magnetic field and, the induced current in the loop at

t = 3

s is

\frac{\alpha}{50}

A. The value of

\alpha

is ________. (Take

\pi = 22/7

)

Q9·PhysicsSingle correctJEE Main 2026

A circular current loop of radius

R

is placed inside square loop of side length

L

(L >> R)

such that they are co-planar and their centers coincide. The permeability of free space is

\mu_0

. The mutual inductance between circular loop and square loop is ________.

(A) $2\sqrt{2}\,\frac{\mu_0 L^2}{R}$
(B) $\sqrt{2}\,\frac{\mu_0 L^2}{R}$
(C) $\sqrt{2}\,\frac{\mu_0 R^2}{L}$
(D) $2\sqrt{2}\,\frac{\mu_0 R^2}{L}$

Q10·PhysicsSingle correctJEE Main 2026

When a coil is placed in a time dependent magnetic field the power dissipated in it is

P

. The number of turns, area of the coil and radius of the coil wire are

N

,

A

and

r

respectively. For a second coils number of turns, area of the coil and radius of the coil wire are

2N

,

2A

and

3r

respectively. When the first coil is replaced with second coil the power dissipated in it is

\sqrt{2}\,\alpha P

. The value of

\alpha

is ______.

(A)36
(B) $128\sqrt{2}$
(C)16
(D)64

Q11·PhysicsSingle correctJEE Main 2026

A 20 m long uniform copper wire held horizontally is allowed to fall under the gravity (g = 10 m/s

^2

) through a uniform horizontal magnetic field of 0.5 Gauss perpendicular to the length of the wire. The induced EMF across the wire it travells a vertical distance of 200 m is ______ mV.

(A) $0.2\sqrt{10}$
(B) $20\sqrt{10}$
(C) $2\sqrt{10}$
(D) $200\sqrt{10}$

Q12·PhysicsSingle correctJEE Main 2026

Suppose a long solenoid of 100 cm length, radius 2 cm having 500 turns per unit length, carries a current

I

= 10 sin (ωt) A, where ω = 1000 rad./s. A circular conducting loop (B) of radius 1 cm coaxially slided through the solenoid at a speed v = 1 cm/s. The r.m.s. current through the loop when the coil B is inserted 10 cm inside the solenoid is

\alpha/\sqrt{2}

μA. The value of α is __________. [Resistance of the loop = 10 Ω]

(A)197
(B)80
(C)280
(D)100

Q13·PhysicsNumericalJEE Main 2026

A simple pendulum made of mass 10 g and a metallic wire of length 10 cm is suspended vertically in a uniform magnetic field of 2 T. The magnetic field direction is perpendicular to the plane of oscillations of the pendulum. If the pendulum is released from an angle of 60° with vertical, then maximum induced EMF between the point of suspension and point of oscillation is ______ mV. (Take g = 10 m/s

^2

)

Q14·PhysicsSingle correctJEE Main 2026

A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop in 0.5 s. The EMF induced in the loop is ___________ mV.

(A)6.6
(B)13.2
(C)8.25
(D)1.32

Q15·PhysicsNumericalJEE Main 2026

Inductance of a coil with

10^4

turns is 10 mH and it is connected to a dc source of 10 V with internal resistance of 10Ω. The energy density in the inductor when the current reaches

\left(\frac{1}{e}\right)

of its maximum value is

\alpha\pi \times \frac{1}{e^2}

J/m

^3

. The value of α is ____. (

\mu_0 = 4\pi \times 10^{-7}

Tm/A).

Q16·PhysicsNumericalJEE Main 2026

A conducting circular loop is rotated about its diameter at a constant angular speed of 100 rad/s in a magnetic field of 0.5T perpendicular to the axis of rotation. When the loop is rotated by 30° from the horizontal position, the induced EMF is 15.4 mV. The radius of the loop is _______ mm.

\left(\text{Take } \pi = \dfrac{22}{7}\right)

Q17·PhysicsSingle correctJEE Main 2026

Three identical coils

C_1

,

C_2

and

C_3

are closely placed such that they share a common axis.

C_2

is exactly midway.

C_1

carries current

I

in anti-clockwise direction while

C_3

carries current

I

in clockwise direction. An induced current flows through

C_2

will be in clockwise direction when

(A) $C_1$ and $C_3$ move with equal speeds away from $C_2$
(B) $C_1$ moves towards $C_2$ and $C_3$ moves away from $C_2$
(C) $C_1$ moves away from $C_2$ and $C_3$ moves towards $C_2$
(D) $C_1$ and $C_3$ move with equal speeds towards $C_2$

Q18·PhysicsSingle correctJEE Main 2026

Figure shows the circuit that contains three resistances (9 Ω each) and two inductors (4 mH each). The reading of ammeter at the moment switch K is turned ON, is _________A.

(A)1
(B)zero
(C)3
(D)2

Q19·PhysicsSingle correctJEE Main 2026

XPQY is a vertical smooth long loop having a total resistance R where PX is parallel to QY and separation between them is

l

. A constant magnetic field B perpendicular to the plane of the loop exists in the entire space. A rod CD of length L (L >

l

) and mass m is made to slide down from rest under the gravity as shown in figure. The terminal speed acquired by the rod is_________m/s. (g = acceleration due to gravity)

(A) $\frac{2mgR}{B^{2}l^{2}}$
(B) $\frac{8mgR}{B^{2}l^{2}}$
(C) $\frac{2mgR}{B^{2}L^{2}}$
(D) $\frac{mgR}{B^{2}l^{2}}$

Q20·PhysicsSingle correctJEE Main 2026

A conducting circular loop of area 1.0

\mathrm{m}^{2}

is placed perpendicular to a magnetic field which varies as B = sin(100 t) Tesla. If the resistance of the loop is 100 Ω , then the average thermal energy dissipated in the loop in one period is _______J.

(A) $\frac{\pi}{2}$
(B) $2\pi$
(C) $\pi$
(D) $\pi^{2}$

Q21·PhysicsSingle correctJEE Main 2026

A 1 m long metal rod AB completes the circuit as shown in figure. The area of circuit is perpendicular to the magnetic field of 0.10 T. If the resistance of the total circuit is 2Ω then the force needed to move the rod towards right with constant speed (v) of 1.5 m/s is _________ N.

(A) $7.5 \times 10^{-2}$
(B) $5.7 \times 10^{-3}$
(C) $5.7 \times 10^{-2}$
(D) $7.5 \times 10^{-3}$

Q22·PhysicsSingle correctJEE Advanced 2025

A conducting square loop initially lies in the XZ plane with its lower edge hinged along the X-axis. Only in the region y ≥ 0, there is a time dependent magnetic field pointing along the z-direction,

\vec{B}(t) = B_{0}(\cos\omega t)\hat{k}

, where

B_{0}

is a constant. The magnetic field is zero everywhere else. At time t = 0, the loop starts rotating with constant angular speed

\omega

about the X axis in the clockwise direction as viewed from the +X axis (as shown in the figure). Ignoring self-inductance of the loop and gravity, which of the following plots correctly represents the induced e.m.f. (V) in the loop as a function of time:

(A)(A)
(B)(B)
(C)(C)
(D)(D)

Q23·PhysicsMultiple correctJEE Advanced 2025

A conducting square loop of side L, mass M and resistance R is moving in the XY plane with its edges parallel to the X and Y axes. The region y ≥ 0 has a uniform magnetic field,

\vec{B} = B_{0}\hat{k}

. The magnetic field is zero everywhere else. At time t = 0, the loop starts to enter the magnetic field with an initial velocity

v_{0}\hat{j}

m/s, as shown in the figure. Considering the quantity

K = \frac{B_{0}^{2}L^{2}}{RM}

in appropriate units, ignoring self-inductance of the loop and gravity, which of the following statements is/are correct:

(A)If $v_{0}$ = 1.5 KL, the loop will stop before it enters completely inside the region of magnetic field.
(B)When the complete loop is inside the region of magnetic field, the net force acting on the loop is zero.
(C)If $v_{0} = \frac{KL}{10}$ , the loop comes to rest at $t = \left(\frac{1}{K}\right)\ln\left(\frac{5}{2}\right)$ .
(D)If $v_{0}$ = 3KL, the complete loop enters inside the region of magnetic field at time $t = \left(\frac{1}{K}\right)\ln\left(\frac{3}{2}\right)$ .

Q24·PhysicsIntegerJEE Main 2025

An inductor of self inductance 1 H connected in series with a resistor of

100\pi\ \Omega

and an AC supply of

100\pi

volt, 50 Hz. Maximum current flowing in the circuit is ______ A.

Q25·PhysicsIntegerJEE Main 2025

Conductor wire ABCDE with each arm 10 cm in length is placed in magnetic field of

\dfrac{1}{\sqrt{2}}

Tesla, perpendicular to its plane. When conductor is pulled towards right with constant velocity of 10 cm/s, induced emf between points A and E is ______ mV.

Q26·PhysicsSingle correctJEE Main 2025

A solenoid having area A and length

l

is filled with a material having relative permeability 2. The magnetic energy stored in the solenoid is:

(A) $\dfrac{B^2Al}{\mu_0}$
(B) $\dfrac{B^2Al}{2\mu_0}$
(C) $B^2Al$
(D) $\dfrac{B^2Al}{4\mu_0}$

Q27·PhysicsSingle correctJEE Main 2025

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury tube, the tube will be damaged. Reason (R): By using the choke coil, the voltage across the tube is reduced by a factor

\dfrac{R}{\sqrt{R^2+\omega^2 L^2}}

, where

\omega

is frequency of the supply across resistor R and inductor L. If the choke coil were not used, the voltage across the resistor would be the same as the applied voltage. In the light of the above statements, choose the most appropriate answer from the options given below:

(A)Both (A) and (R) are true but (R) is not the correct explanation of (A).
(B)(A) is false but (R) is true.
(C)Both (A) and (R) are true and (R) is the correct explanation of (A).
(D)(A) is true but (R) is false.

Q28·PhysicsSingle correctJEE Main 2025

Consider

I_1

and

I_2

are the currents flowing simultaneously in two nearby coils 1 & 2, respectively. If

L_1

= self inductance of coil 1,

M_{12}

= mutual inductance of coil 1 with respect to coil 2, then the value of induced emf in coil 1 will be

(A) $\varepsilon_1=-L_1\dfrac{dI_1}{dt}+M_{12}\dfrac{dI_2}{dt}$
(B) $\varepsilon_1=-L_1\dfrac{dI_1}{dt}-M_{12}\dfrac{dI_1}{dt}$
(C) $\varepsilon_1=-L_1\dfrac{dI_1}{dt}-M_{12}\dfrac{dI_2}{dt}$
(D) $\varepsilon_1=-L_1\dfrac{dI_2}{dt}-M_{12}\dfrac{dI_1}{dt}$

Q29·PhysicsSingle correctJEE Main 2025

A coil of area A and N turns is rotating with angular velocity

\omega

in a uniform magnetic field

\vec{B}

about an axis perpendicular to

\vec{B}

. Magnetic flux

\phi

and induced emf

\varepsilon

across it, at an instant when

\vec{B}

is parallel to the plane of coil, are:

(A) $\phi=AB,\ \varepsilon=0$
(B) $\phi=0,\ \varepsilon=NAB\omega$
(C) $\phi=0,\ \varepsilon=0$
(D) $\phi=AB,\ \varepsilon=NAB\omega$

Q30·PhysicsSingle correctJEE Main 2025

A uniform magnetic field of 0.4 T acts perpendicular to a circular copper disc 20 cm in radius. The disc is having a uniform angular velocity of

10\pi

rad s

^{-1}

about an axis through its centre and perpendicular to the disc. What is the potential difference developed between the axis of the disc and the rim? (

\pi=3.14

)

(A)0.0628 V
(B)0.5024 V
(C)0.2512 V
(D)0.1256 V

Q31·PhysicsIntegerJEE Main 2025

A conducting bar moves on two conducting rails as shown in the figure. A constant magnetic field B exists into the page. The bar starts to move from the vertex at time t = 0 with a constant velocity. If the induced EMF is

E\propto t^n

, then value of n is ______.

Q32·PhysicsSingle correctJEE Main 2025

Regarding self-inductance : A : The self-inductance of the coil depends on its geometry. B : Self-inductance does not depend on the permeability of the medium. C : Self-induced e.m.f. opposes any change in the current in a circuit. D : Self-inductance is electromagnetic analogue of mass in mechanics. E : Work needs to be done against self-induced e.m.f. in establishing the current. Choose the correct answer from the options given below:

(A)A, B, C, D only
(B)A, C, D, E only
(C)A, B, C, E only
(D)B, C, D, E only

Q33·PhysicsSingle correctJEE Main 2025

A rectangular metallic loop is moving out of a uniform magnetic field region to a field free region with a constant speed. When the loop is partially inside the magnetic field, the plot of magnitude of induced emf (

\varepsilon

) with time (t) is given by

(A)(1)
(B)(2)
(C)(3)
(D)(4)

Q34·PhysicsSingle correctJEE Advanced 2024

A region in the form of an equilateral triangle (in

x-y

plane) of height L has a uniform magnetic field

\vec{B}

pointing in the

+z

-direction. A conducting loop PQR , in the form of an equilateral triangle of the same height L , is placed in the

x-y

plane with its vertex P at

x = 0

in the orientation shown in the figure. At

t = 0

, the loop starts entering the region of the magnetic field with a uniform velocity

\vec{v}

along the

+x

-direction. The plane of the loop and its orientation remain unchanged throughout its motion.

(A)(A)
(B)(B)
(C)(C)
(D)(D)

Q35·PhysicsSingle correctJEE Main 2024

A square loop of side 15 cm is being moved towards right at a constant speed of 2 cm/s as shown in the figure. The front edge enters the 50 cm wide magnetic field at

t=0

. The value of induced emf in the loop at

t=10

s will be:

(A)0.3 mV
(B)4.5 mV
(C)0 mV
(D)3 mV

Q36·PhysicsNumericalJEE Main 2024

A square loop PQRS having

10

turns, area

3.6\times10^{-3}\,m^2

and resistance

100\,\Omega

is slowly and uniformly being pulled out of a uniform magnetic field of magnitude

B=0.5

T as shown. Work done in pulling the loop out of the field in

1.0

s is ___

\times10^{-6}

J.

Q37·PhysicsSingle correctJEE Main 2024

In a coil, the current changes form

-2

A to

+2

A in 0.2 s and induces an emf of 0.1 V. The self-inductance of the coil is :

(A)5 mH
(B)1 mH
(C)2.5 mH
(D)4 mH

Q38·PhysicsSingle correctJEE Main 2024

Two conducting circular loops A and B are placed in the same plane with their centres coinciding as shown in the figure (radius of A is

a

, radius of B is

b

, with

b \gg a

). The mutual inductance between them is:

(A) $\dfrac{\mu_0\pi a^2}{2b}$
(B) $\dfrac{\mu_0}{2\pi}\dfrac{b^2}{a}$
(C) $\dfrac{\mu_0\pi b^2}{2a}$
(D) $\dfrac{\mu_0}{2\pi}\dfrac{a^2}{b}$

Q39·PhysicsNumericalJEE Main 2024

The current in an inductor is given by

I=(3t+8)

, where

t

is in seconds. The magnitude of the induced emf produced in the inductor is 12 mV. The self-inductance of the inductor is __________ mH.

Q40·PhysicsNumericalJEE Main 2024

A rod of length 60 cm rotates with a uniform angular velocity 20 rad s

^{-1}

about its perpendicular bisector, in a uniform magnetic field 0.5 T. The direction of magnetic field is parallel to the axis of rotation. The potential difference between the two ends of the rod is ______ V.

Q41·PhysicsNumericalJEE Main 2024

A rectangular loop of sides

12\,cm

and

5\,cm

, with its sides parallel to the x-axis and y-axis respectively moves with a velocity of

5\,cm/s

in the positive x axis direction, in a space containing a variable magnetic field in the positive z direction. The field has a gradient of

10^{-3}\,T/cm

along the negative x direction and it is decreasing with time at the rate of

10^{-3}\,T/s

. If the resistance of the loop is

6\,m\Omega

, the power dissipated by the loop as heat is ___

\times10^{-9}\,W

.

Q42·PhysicsNumericalJEE Main 2024

A coil of 200 turns and area 0.20 m

^2

is rotated at half a revolution per second and is placed in uniform magnetic field of 0.01 T perpendicular to axis of rotation of the coil. The maximum voltage generated in the coil is

\dfrac{2\pi}{\beta}

volt. The value of

\beta

is __________.

Q43·PhysicsSingle correctJEE Main 2024

A coil is placed perpendicular to a magnetic field of 5000 T. When the field is changed to 3000 T in 2s, an induced emf of 22 V is produced in the coil. If the diameter of the coil is 0.02 m, then the number of turns in the coil is :

(A)7
(B)70
(C)35
(D)140

Q44·PhysicsNumericalJEE Main 2024

A small square loop of wire of side

\ell

is placed inside a large square loop of wire of side L

(L=\ell^2)

. The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is

\sqrt{x}\times10^{-7}

H, where

x=

______.

Q45·PhysicsNumericalJEE Main 2024

The magnetic flux

\phi

(in weber) linked with a closed circuit of resistance

8\,\Omega

varies with time (in seconds) as

\phi=5t^2-36t+1

. The induced current in the circuit at

t=2

s is ______ A.

Q46·PhysicsNumericalJEE Main 2024

A ceiling fan having

3

blades of length

80\,cm

each is rotating with an angular velocity of

1200\,rpm

. The magnetic field of earth in that region is

0.5\,G

and angle of dip is

30^\circ

. The emf induced across the blades is

N\pi\times10^{-5}\,V

. The value of

N

is ___

Q47·PhysicsSingle correctJEE Main 2024

A capacitor of capacitance

100\,\mu

F is charged to a potential of 12 V and connected to a 6.4 mH inductor to produce oscillations. The maximum current in the circuit would be :

(A) $3.2$ A
(B) $1.5$ A
(C) $2.0$ A
(D) $1.2$ A

Q48·PhysicsNumericalJEE Main 2024

A horizontal straight wire 5 m long extending from east to west is falling freely at right angle to horizontal component of earth's magnetic field

0.60\times10^{-4}

Wbm

^{-2}

. The instantaneous value of emf induced in the wire when its velocity is 10 ms

^{-1}

is ___

\times10^{-3}

V.

Q49·PhysicsNumericalJEE Main 2024

A square loop of side 10 cm and resistance

0.7\,\Omega

is placed vertically in east-west plane. A uniform magnetic field of 0.20 T is set up across the plane in north east direction. The magnetic field is decreased to zero in 1 s at a steady rate. Then, magnitude of induced emf is

\sqrt{x}\times10^{-3}

V. The value of x is ______ .

Q50·PhysicsSingle correctJEE Main 2024

In an a.c. circuit, voltage and current are given by:

V=100\sin(100\,t)

V and

I=100\sin\left(100\,t+\dfrac{\pi}{3}\right)

mA respectively. The average power dissipated in one cycle is:

(A)5 W
(B)10 W
(C)2.5 W
(D)25 W

Q51·PhysicsNumericalJEE Main 2024

Two coils have mutual inductance 0.002 H. The current changes in the first coil according to the relation

i=i_0\sin\omega t

, where

i_0=5

A and

\omega=50\pi

rad/s. The maximum value of emf in the second coil is

\dfrac{\pi}{\alpha}

V. The value of

\alpha

is __________.

Q52·PhysicsSingle correctJEE Main 2024

A rectangular loop of length 2.5 m and width 2 m is placed at

60^{\circ}

to a magnetic field of 4 T. The loop is removed from the field in 10 sec. The average emf induced in the loop during this time is:

(A) $-2$ V
(B) $+2$ V
(C) $+1$ V
(D) $-1$ V

Q53·PhysicsSingle correctJEE Advanced 2023

A thin conducting rod MN of mass 20 gm, length 25 cm and resistance 10

\Omega

is held on frictionless, long, perfectly conducting vertical rails as shown in the figure. There is a uniform magnetic field

B_0 = 4

T directed perpendicular to the plane of the rod-rail arrangement. The rod is released from rest at time t = 0 and it moves down along the rails. Assume air drag is negligible. Match each quantity in List-I with an appropriate value from List-II, and choose the correct option. [Given: The acceleration due to gravity g = 10 m

s^{-2}

and

e^{-1} = 0.4

]

List-I	List-II
P.At $t = 0.2$ s, the magnitude of the induced emf in Volt	1.0.07
Q.At $t = 0.2$ s, the magnitude of the magnetic force in Newton	2.0.14
R.At $t = 0.2$ s, the power dissipated as heat in Watt	3.1.20
S.The magnitude of terminal velocity of the rod in m $s^{-1}$	4.0.12
	5.2.00

(A)P $\rightarrow$ 5, Q $\rightarrow$ 2, R $\rightarrow$ 3, S $\rightarrow$ 1
(B)P $\rightarrow$ 3, Q $\rightarrow$ 1, R $\rightarrow$ 4, S $\rightarrow$ 5
(C)P $\rightarrow$ 4, Q $\rightarrow$ 3, R $\rightarrow$ 1, S $\rightarrow$ 2
(D)P $\rightarrow$ 3, Q $\rightarrow$ 4, R $\rightarrow$ 2, S $\rightarrow$ 5

Q54·PhysicsIntegerJEE Advanced 2023

A rectangular conducting loop of length 4 cm and width 2 cm is in the xy-plane, as shown in the figure. It is being moved away from a thin and long conducting wire along the direction

\frac{\sqrt{3}}{2}\hat{x} + \frac{1}{2}\hat{y}

with a constant speed v. The wire is carrying a steady current

I

= 10 A in the positive x-direction. A current of 10

\mu

A flows through the loop when it is at a distance d = 4 cm from the wire. If the resistance of the loop is 0.1

\Omega

, then the value of v is ________ m s

^{-1}

. [Given: The permeability of free space

\mu_0 = 4\pi\times10^{-7}

N A

^{-2}

]

Q55·PhysicsNumericalJEE Main 2023

A

20

cm long metallic rod is rotated with

210

rpm about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field

0.2

T parallel to the axis exists everywhere. The emf developed between the centre and the ring is __________ mV. Take

\pi = \frac{22}{7}

.

Q56·PhysicsSingle correctJEE Main 2023

A 12 V battery connected to a coil of resistance 6

\Omega

through a switch, drives a constant current in the circuit. The switch is opened in 1 ms. The emf induced across the coil is 20 V. The inductance of the coil is :

(A)5 mH
(B)12 mH
(C)8 mH
(D)10 mH

Q57·PhysicsSingle correctJEE Main 2023

Which of the following Maxwell's equations is valid for time varying conditions but not valid for static conditions:

(A) $\displaystyle\oint\vec B\cdot d\vec l=\mu_{0}I$
(B) $\displaystyle\oint\vec E\cdot d\vec l=0$
(C) $\displaystyle\oint\vec E\cdot d\vec l=-\dfrac{\partial\Phi_{B}}{\partial t}$
(D) $\displaystyle\oint\vec D\cdot d\vec A=Q$

Q58·PhysicsNumericalJEE Main 2023

In the given figure, an inductor and a resistor are connected in series with a battery of emf

E

volt.

\dfrac{E^{2}}{2b}\,J/s

represents the maximum rate at which the energy is stored in the magnetic field (inductor). The numerical value of

\dfrac{b}{a}

will be _____.

Q59·PhysicsNumericalJEE Main 2023

An insulated copper wire of 100 turns is wrapped around a wooden cylindrical core of the cross-sectional area 24 cm

^2

. The two ends of the wire are connected to a resistor. The total resistance in the circuit is 12

\Omega

. If an externally applied uniform magnetic field in the core along its axis changes from 1.5 T in one direction to 1.5 T in the opposite direction, the charge flowing through a point in the circuit during the change of magnetic field will be ____ mC.

Q60·PhysicsNumericalJEE Main 2023

A conducting circular loop is placed in a uniform magnetic field of 0.4 T with its plane perpendicular to the field. Somehow, the radius of the loop starts expanding at a constant rate of 1 mm/s. The magnitude of induced emf in the loop at an instant when the radius of the loop is 1 cm will be _________

\mu

V.

Q61·PhysicsSingle correctJEE Main 2023

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: A bar magnet dropped through a metallic cylindrical pipe takes more time to come down compared to a non-magnetic bar with the same geometry and mass. Reason R: For the magnetic bar, eddy currents are produced in the metallic pipe which oppose the motion of the magnetic bar. In the light of the above statements, choose the correct answer from the options given below.

(A)Both A and R are true but R is NOT the correct explanation of A
(B)A is true but R is false
(C)Both A and R are true and R is the correct explanation of A
(D)A is false but R is true

Q62·PhysicsNumericalJEE Main 2023

A metallic cube of side

15

cm is moving along the y-axis at a uniform velocity of

2

ms

^{-1}

in a region of uniform magnetic field of magnitude

0.5

T directed along the z-axis. In equilibrium the potential difference between the faces of higher and lower potential developed because of the motion through the field will be ____ mV.

Q63·PhysicsNumericalJEE Main 2023

The magnetic field B crossing normally a square metallic plate of area 4

\text{m}^2

is changing with time as shown in figure. The magnitude of induced emf in the plate during

t = 2

s to

t = 4

s, is ________ mV

Q64·PhysicsNumericalJEE Main 2023

A coil has an inductance of

2

H and resistance of

4\ \Omega

. A

10

V supply is applied across the coil. The energy stored in the magnetic field after the current has built up to its equilibrium value will be ____

\times10^{-3}

J.

Q65·PhysicsNumericalJEE Main 2023

A square loop of side

2.0

cm is placed inside a long solenoid that has

50

turns per centimetre and carries a sinusoidally varying current of amplitude

2.5

A and angular frequency

700

rad s

^{-1}

. The central axes of the loop and the solenoid coincide. The amplitude of the emf induced in the loop is

x\times10^{-4}

V. The value of x is _______ (take

\pi=\tfrac{22}{7}

).

Q66·PhysicsNumericalJEE Main 2023

A 1m long metal rod XY completes the circuit as shown in figure. The plane of the circuit is perpendicular to the magnetic field of flux density 0.15 T. If the resistance of the circuit is

5\,\Omega

, the force needed to move the rod in direction, as indicated, with a constant speed of 4 m/s will be _________

\times10^{-3}

N.

Q67·PhysicsSingle correctJEE Main 2023

A bar magnet is released from rest along the axis of a very long vertical copper tube. After some time the magnet will:

(A)Move down with almost constant speed
(B)Oscillate inside the tube
(C)Move down with an acceleration greater than g
(D)Move down with an acceleration equal to g

Q68·PhysicsSingle correctJEE Main 2023

An emf of 0.08 V is induced in a metal rod of length 10 cm held normal to a uniform magnetic field of 0.4 T, when it moves with a velocity of:

(A)2 ms $^{-1}$
(B)3.2 ms $^{-1}$
(C)0.5 ms $^{-1}$
(D)20 ms $^{-1}$

Q69·PhysicsSingle correctJEE Main 2023

The induced emf can be produced in a coil by A. moving the coil with uniform speed inside uniform magnetic field B. moving the coil with non-uniform speed inside uniform magnetic field C. rotating the coil inside the uniform magnetic field D. changing the area of the coil inside the uniform magnetic field Choose the correct answer from the options given below:

(A)B and D only
(B)B and C only
(C)A and C only
(D)C and D only

Q70·PhysicsNumericalJEE Main 2023

Two concentric circular coils with radii 1 cm and 1000 cm, and number of turns 10 and 200 respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be ____

\times 10^{-8}

H. (Take

\pi^2=10

)

Q71·PhysicsSingle correctJEE Main 2023

Match List I (electrical machines and resonance phenomena) with List II (the underlying principle or condition). Choose the correct answer from the options given below:

List I	List II
A.AC generator	I.Presence of both L and C
B.Transformer	II.Electromagnetic Induction
C.Resonance phenomenon to occur	III.Quality factor
D.Sharpness of resonance	IV.Mutual Induction

(A)A-IV, B-III, C-I, D-II
(B)A-IV, B-II, C-I, D-III
(C)A-II, B-IV, C-I, D-III
(D)A-II, B-I, C-III, D-IV

Q72·PhysicsNumericalJEE Main 2023

A square shaped coil of area

70

cm

^2

having

600

turns rotates in a magnetic field of

0.4

wbm

^{-2}

, about an axis which is parallel to one of the side of the coil and perpendicular to the direction of field. If the coil completes

500

revolution in a minute, the instantaneous emf when the plane of the coil is inclined at

60°

with the field, will be _________ V. (Take

\pi=\dfrac{22}{7}

)

Q73·PhysicsSingle correctJEE Main 2023

A coil is wrapped in magnetic field such that plane of coil is perpendicular to the direction of magnetic field. The magnetic flux through a coil can be changed: A. By changing the magnitude of the magnetic field within the coil. B. By changing the area of coil within the magnetic field. C. By changing the angle between the direction of magnetic field and the plane of the coil. D. By reversing the magnetic field direction abruptly without changing its magnitude. Choose the most appropriate answer from the options given below:

(A)A and B only
(B)A, B and D only
(C)B, C and D only
(D)A and C only

Q74·PhysicsSingle correctJEE Main 2023

Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height. Choose the correct statement out of the following Assume negligible air friction)

(A)Insulating ball will reach the earth's surface earlier than the metal ball
(B)Metal ball will reach the earth's surface earlier than the insulating ball
(C)Both will reach the earth's surface simultaneously
(D)Time taken by them to reach the earth's surface will be independent of the properties of their materials

Q75·PhysicsNumericalJEE Main 2023

In an ac generator, a rectangular coil of 100 turns each having area

14\times10^{-2}

m

^2

is rotated at 360 rev/min about an axis perpendicular to a uniform magnetic field of magnitude 3.0 T. The maximum value of the emf produced will be _______ V. (Take

\pi=\dfrac{22}{7}

)

Q76·PhysicsNumericalJEE Main 2023

As per the given figure, if

\dfrac{dI}{dt}=-1

A/s then the value of

V_{AB}

at this instant will be _________ V.

Q77·PhysicsSingle correctJEE Main 2023

A square loop of area

25\,cm^2

has a resistance of

10\,\Omega

. The loop is placed in uniform magnetic field of magnitude

40.0\,T

. The plane of loop is perpendicular to the magnetic field. The work done in pulling the loop out of the magnetic field slowly and uniformly in

1.0\,sec

, will be:

(A) $1.0\times10^{-3}\,J$
(B) $2.5\times10^{-3}\,J$
(C) $5\times10^{-3}\,J$
(D) $1.0\times10^{-4}\,J$

Q78·PhysicsSingle correctJEE Main 2023

Find the mutual inductance in the arrangement, when a small circular loop of wire of radius

R

is placed inside a large square loop of wire of side

L

(

L \gg R

). The loops are coplanar and their centers coincide:

(A) $M=\dfrac{\sqrt{2}\,\mu_0 R^2}{L}$
(B) $M=\dfrac{2\sqrt{2}\,\mu_0 R}{L^2}$
(C) $M=\dfrac{\sqrt{2}\,\mu_0 R}{L^2}$
(D) $M=\dfrac{2\sqrt{2}\,\mu_0 R^2}{L}$

Q79·PhysicsNumericalJEE Main 2023

A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field

B = 0.8

T. When released the radius of the loop starts shrinking at a constant rate of 2 cm s

^{-1}

. The induced emf in the loop at an instant when the radius of the loop is 10 cm will be ________ mV.

Q80·PhysicsSingle correctJEE Main 2023

A wire of length

1

m moving with velocity

8

m/s at right angles to a magnetic field of

2

T. The magnitude of induced emf, between the ends of wire will be

(A) $20$ V
(B) $8$ V
(C) $12$ V
(D) $16$ V

Q81·PhysicsSingle correctJEE Main 2023

A metallic rod of length '

L

' is rotated with an angular speed of '

\omega

' normal to a uniform magnetic field '

B

' about an axis passing through one end of rod as shown in figure. The induced emf will be:

(A) $\dfrac14 BL^2\omega$
(B) $\dfrac12 B^2 L^2\omega$
(C) $\dfrac14 B^2 L\omega$
(D) $\dfrac12 BL^2\omega$

Q82·PhysicsSingle correctJEE Main 2023

A conducting circular loop of radius

\tfrac{10}{\sqrt{\pi}}

cm is placed perpendicular to a uniform magnetic field of 0.5 T. The magnetic field is decreased to zero in 0.5 s at a steady rate. The induced emf in the circular loop at 0.25 s is:

(A)emf = 1 mV
(B)emf = 5 mV
(C)emf = 100 mV
(D)emf = 10 mV

Q83·PhysicsNumericalJEE Main 2023

Three identical resistors with resistance

R=12\,\Omega

and two identical inductors with self inductance

L=5

mH are connected to an ideal battery with emf of

12

V as shown in figure. The current through the battery long after the switch has been closed will be _________ A.

Q84·PhysicsSingle correctJEE Main 2022

A coil of inductance 1 H and resistance 100 Ω is connected to a battery of 6 V. Determine approximately : (a) The time elapsed before the current acquires half of its steady – state value (b) The energy stored in the magnetic field associated with the coil at an instant 15 ms after the circuit is switched on. (Given In2 = 0.693,

e^{-3/2} = 0.25

)

(A)t = 10 ms; U = 2 mJ
(B)t = 10 ms; U = 1 mJ
(C)t = 7 ms; U = 1 mJ
(D)t = 7 ms; U = 2 mJ

Q85·PhysicsNumericalJEE Main 2022

For the given circuit the current through battery of 6 V just after closing the switch 'S' will be ......... A.

Q86·PhysicsNumericalJEE Main 2022

A conducting circular loop is placed in X − Y plane in presence of magnetic field

\vec{B} = \left(3t^{3}\hat{j} + 3t^{2}\hat{k}\right)

in SI unit. If the radius of the loop is 1m, the induced emf in the loop, at time, t = 2s is nπV. The value of n is……..

Q87·PhysicsNumericalJEE Main 2022

In a coil of resistance

8\Omega

, the magnetic flux due to an external magnetic field varies with time as

\phi = \frac{2}{3}\left(9 - t^2\right)

. The value of total heat produced in the coil, till the flux becomes zero, will be________J.

Q88·PhysicsSingle correctJEE Main 2022

A small square loop of wire of side

l

is placed inside a large square loop of wire L (L >>

l

). Both loops are coplanar and their centres coincide at point O as shown in figure. The mutual inductance of the system is :

(A) $\frac{2\sqrt{2}\mu_0 L^{2}}{\pi \ell}$
(B) $\frac{\mu_0 \ell^{2}}{2\sqrt{2}\pi L}$
(C) $\frac{2\sqrt{2}\mu_0 \ell^{2}}{\pi L}$
(D) $\frac{\mu_0 L^{2}}{2\sqrt{2}\pi \ell}$

Q89·PhysicsSingle correctJEE Main 2022

A coil is placed in a time varying magnetic field. If the number of turns in the coil were to be halved and the radius of wire doubled, the electrical power dissipated due to the current induced in the coil would be: (Assume the coil to be short circuited.)

(A)Halved
(B)Quadrupled
(C)The same
(D)Doubled

Q90·PhysicsNumericalJEE Main 2022

A metallic rod of length 20 cm is palced in North-South direction and is moved at a constant speed of 20 m/s towards East. The horizontal component of the Earth's magnetic field at that place is

4 \times 10^{-3}

T and the angle of dip is 45°. The emf induced in the rod is ________ mV.

Q91·PhysicsSingle correctJEE Main 2022

A metallic conductor of length 1m rotates in a vertical plane parallel to east-west direction about one of its end with angular velocity 5 rad/s. If the horizontal component of earth's magnetic field is

0.2 \times 10^{-4}

T, then emf induced between the two ends of the conductor is :

(A)5μV
(B)50μV
(C)5mV
(D)50mV

Q92·PhysicsNumericalJEE Main 2022

A 10Ω, 20 mH coil carrying constant current is connected to a battery of 20 V through a switch is opened current becomes zero in 100μs. The average emf induced in the coil is ............ V.

Q93·PhysicsSingle correctJEE Main 2022

Two coils of self inductance

L_1

and

L_2

are connected in series combination having mutual inductance of the coils as M. The equivalent self inductance of the combination will be :

(A) $\frac{1}{L_1} + \frac{1}{L_2} + \frac{1}{M}$
(B) $L_1 + L_2 + M$
(C) $L_1 + L_2 + 2M$
(D) $L_1 + L_2 - 2M$

Q94·PhysicsNumericalJEE Main 2022

The current in a coil of self inductance 2.0 H is increasing according to

I = 2\sin(t^{2})

A. The amount of energy spent during the period when current changes from 0 to 2A is ______ J.

Q95·PhysicsSingle correctJEE Main 2022

Match List-I with List-II List-I List-II (A) AC generator (I) Detects the presence of current in the circuit (B) Galvanometer (II) Converts mechanical energy into electrical energy (C) Transformer (III) Works on the principle of resonance in AC circuit (D) Metal detector (IV) Changes an alternating voltage for smaller or greater value Choose the correct answer from the options given below :-

(A)(A)–(II), B–(I), (C)–(IV), (D)–(III)
(B)(A)–(II), B–(I), (C)–(III), (D)–(IV)
(C)(A)–(III), B–(IV), (C)–(II), (D)–(I)
(D)(A)–(III), B–(I), (C)–(II), (D)–(IV)

Q96·PhysicsNumericalJEE Main 2022

A circular coil of 1000 turns each with area 1m

^2

is rotated about its vertical diameter at the rate of one revolution per second in a uniform horizontal magnetic field of 0.07T. The maximum voltage generation will be ______V.

Q97·PhysicsSingle correctJEE Advanced 2021

A special metal S conducts electricity without any resistance. A closed wire loop, made of S, does not allow any change in flux through itself by inducing a suitable current to generate a compensating flux. The induced current in the loop cannot decay due to its zero resistance. This current gives rise to a magnetic moment which in turn repels the source of magnetic field or flux. Consider such a loop, of radius

a

, with its center at the origin. A magnetic dipole of moment

m

is brought along the axis of this loop from infinity to a point at distance

r

(>>

a

) from the center of the loop with its north pole always facing the loop, as shown in the figure below. The magnitude of magnetic field of a dipole

m

, at a point on its axis at distance

r

, is

\frac{\mu_0}{2\pi}\frac{m}{r^3}

, where

\mu_0

is the permeability of free space. The magnitude of the force between two magnetic dipoles with moments,

m_1

and

m_2

, separated by a distance r on the common axis, with their north poles facing each other, is

\frac{km_1m_2}{r^4}

, where

k

is a constant of appropriate dimensions. The direction of this force is along the line joining the two dipoles. The work done in bringing the dipole from infinity to a distance

r

from the center of the loop by the given process is proportional to

(A) $\frac{m}{r^5}$
(B) $\frac{m^2}{r^5}$
(C) $\frac{m^2}{r^6}$
(D) $\frac{m^2}{r^7}$

Q98·PhysicsMultiple correctJEE Advanced 2021

A long straight wire carries a current,

I

= 2 ampere. A semi-circular conducting rod is placed beside it on two conducting parallel rails of negligible resistance. Both the rails are parallel to the wire. The wire, the rod and the rails lie in the same horizontal plane, as shown in the figure. Two ends of the semi-circular rod are at distances 1cm and 4 cm from the wire. At time t = 0, the rod starts moving on the rails with a speed v = 3.0 m/s (see the figure). A resistor R = 1.4

\Omega

and a capacitor

C_0

= 5.0

\mu

F are connected in series between the rails. At time t = 0,

C_0

is uncharged. Which of the following statement(s) is(are) correct ? [

\mu_0 = 4\pi \times 10^{-7}

SI units. Take ln 2 = 0.7]

(A)Maximum current through $R$ is $1.2 \times 10^{-6}$ ampere
(B)Maximum current through $R$ is $3.8 \times 10^{-6}$ ampere
(C)Maximum charge on capacitor $C_0$ is $8.4 \times 10^{-12}$ coulomb
(D)Maximum charge on capacitor $C_0$ is $2.4 \times 10^{-12}$ coulomb

Q99·PhysicsSingle correctJEE Advanced 2021

A special metal S conducts electricity without any resistance. A closed wire loop, made of S, does not allow any change in flux through itself by inducing a suitable current to generate a compensating flux. The induced current in the loop cannot decay due to its zero resistance. This current gives rise to a magnetic moment which in turn repels the source of magnetic field or flux. Consider such a loop, of radius

a

, with its center at the origin. A magnetic dipole of moment

m

is brought along the axis of this loop from infinity to a point at distance

r

(>>

a

) from the center of the loop with its north pole always facing the loop, as shown in the figure below. The magnitude of magnetic field of a dipole

m

, at a point on its axis at distance

r

, is

\frac{\mu_0}{2\pi}\frac{m}{r^3}

, where

\mu_0

is the permeability of free space. The magnitude of the force between two magnetic dipoles with moments,

m_1

and

m_2

, separated by a distance r on the common axis, with their north poles facing each other, is

\frac{km_1m_2}{r^4}

, where

k

is a constant of appropriate dimensions. The direction of this force is along the line joining the two dipoles. When the dipole

m

is placed at a distance

r

from the center of the loop (as shown in the figure), the current induced in the loop will be proportional to

(A) $\frac{m}{r^3}$
(B) $\frac{m^2}{r^2}$
(C) $\frac{m}{r^2}$
(D) $\frac{m^2}{r}$

Q100·PhysicsSingle correctJEE Main 2021

A square loop of side 20 cm and resistance 1Ω is moved towards right with a constant speed v

_{0}

. The right arm of the loop is in a uniform magnetic field of 5T. The field is perpendicular to the plane of the loop and is going into it. The loop is connected to a network of resistors each of value 4Ω. What should be the value of v

_{0}

so that a steady current of 2 mA flows in the loop ?

(A)1 m/s
(B)1 cm/s
(C)10 $^{2}$ m/s
(D)10 $^{-2}$ cm/s

Q101·PhysicsSingle correctJEE Main 2021

For the given circuit the current

i

through the battery when the key in closed and the steady state has been reached is__________.

(A)6 A
(B)25 A
(C)10 A
(D)0 A

Q102·PhysicsSingle correctJEE Main 2021

A small square loop of side 'a' and one turn is placed inside a larger square loop of side b and one turn (b >> a). The two loops are coplanar with their centres coinciding. If a current I is passed in the square loop of side 'b', then the coefficient of mutual inductance between the two loops is :

(A) $\frac{\mu_{0}}{4\pi}8\sqrt{2}\,\frac{a^{2}}{b}$
(B) $\frac{\mu_{0}}{4\pi}\frac{8\sqrt{2}}{a}$
(C) $\frac{\mu_{0}}{4\pi}8\sqrt{2}\,\frac{b^{2}}{a}$
(D) $\frac{\mu_{0}}{4\pi}\frac{8\sqrt{2}}{b}$

Q103·PhysicsSingle correctJEE Main 2021

A coil is placed in a magnetic field

\vec{B}

as shown below : A current is induced in the coil because

\vec{B}

is :

(A)Outward and decreasing with time
(B)Parallel to the plane of coil and decreasing with time
(C)Outward and increasing with time
(D)Parallel to the plane of coil and increasing with time

Q104·PhysicsSingle correctJEE Main 2021

A constant magnetic field of 1 T is applied in the x > 0 region. A metallic circular ring of radius 1m is moving with a constant velocity of 1 m/s along the x-axis. At t = 0s, the centre of O of the ring is at x = − 1m. What will be the value of the induced emf in the ring at t = 1s? (Assume the velocity of the ring does not change.)

(A)1 V
(B)2π V
(C)2 V
(D)0 V

Q105·PhysicsSingle correctJEE Main 2021

An inductor coil stores 64 J of magnetic field energy and dissipates energy at the rate of 640 W when a current of 8A is passed through it. If this coil is joined across an ideal battery, find the time constant of the circuit in seconds :

(A)0.4
(B)0.8
(C)0.125
(D)0.2

Q106·PhysicsNumericalJEE Main 2021

A circular coil of radius 8.0 cm and 20 turns is rotated about its vertical diameter with an angular speed of 50 rad s

^{-1}

in a uniform horizontal magnetic field of

3.0 \times 10^{-2}

T. The maximum emf induced the coil will be ..........

\times 10^{-2}

volt (rounded off to the nearest integer)

Q107·PhysicsNumericalJEE Main 2021

In the given figure the magnetic flux through the loop increases according to the relation φ

_\beta

(t)10t

^2

+ 20t, where φ

_\beta

is in milliwebers and t is in seconds. The magnitude of current throughR = 2Ω resistor at t = 5s is ________ mA.

Q108·PhysicsNumericalJEE Main 2021

Consider an electrical circuit containing a two way switch 'S'. Initially S is open and then

T_1

is connected to

T_2

. As the current in R = 6Ω attains a maximum value of steady state level,

T_1

is disconnected from

T_2

and immediately connected to

T_3

. Potential drop across r = 3Ω resistor immediately after

T_1

is connected to

T_3

is ____ V. (Round off to the Nearest Integer)

Q109·PhysicsNumericalJEE Main 2021

A circular conducting coil of radius 1 m being heated by the change of magnetic field

\vec{B}

passing perpendicular to the plane in which the coil is laid. The resistance of the coil is 2μΩ .The magnetic field is slowly switched off such that its magnitude changes in time as

B = \frac{4}{\pi} \times 10^{-3}\ \text{T}\left(1 - \frac{t}{100}\right)

The energy dissipated by the coil before the magnetic field is switched off completely is E = _________ mJ

Q110·PhysicsNumericalJEE Main 2021

An inductor of 10 mH is connected to a 20 V battery through a resistor of 10kΩ and a switch . After a long time, when maximum current is set up in the circuit, the current is switched off. The current in the circuit after 1 μs is

\frac{x}{100}

mA. Then x is equal to ________. (Take

e^{-1}

= 0.37 )

Q111·PhysicsSingle correctJEE Main 2021

The arm PQ of a rectangular conductor is moving from x = 0 to x = 2b outwards and then inwards from x = 2b to x = 0 as shown in the figure. A uniform magnetic field perpendicular to the plane is acting from x = 0 to x = b. Identify the graph the variation of different quantities with distance.

(A)A − Flux, B − EMF, C − Power dissipated
(B)A − EMF, B − Power dissipated, C − Flux
(C)A − Power dissipated, B − Flux, C − EMF
(D)A − Flux, B − Power dissipated, C − EMF

Q112·PhysicsSingle correctJEE Main 2021

The time taken for the magnetic energy to reach 25% of its maximum value, when a solenoid of resistance R, inductance L is connected to a battery, is :

(A) $\frac{L}{R}\ell n5$
(B)infinite
(C) $\frac{L}{R}\ell n2$
(D) $\frac{L}{R}\ell n10$

Q113·PhysicsSingle correctJEE Main 2021

A conducting bar of length L is free to slide on two parallel conducting rails as shown in the figure Two resistors R

_1

and R

_2

are connected across the ends of the rails. There is a uniform magnetic field

\vec{B}

pointing into the page. An external agent pulls the bar to the left at a constant speed v. The correct statement about the directions of induced currents I

_1

and I

_2

flowing through R

_1

and R

_2

respectively is :

(A)Both I $_1$ and I $_2$ are in anticlockwise direction
(B)Both I $_1$ and I $_2$ are in clockwise direction
(C)I $_1$ is in clockwise direction and I $_2$ is in anticlockwise direction
(D)I $_1$ is in anticlockwise direction and I $_2$ is in clockwise direction

Q114·PhysicsSingle correctJEE Main 2021

The magnetic field in a region is given by

\vec{B} = B_{0}\left(\frac{x}{a}\right)\hat{k}

. A square loop of side d is placed with its edges along the x and y axes. The loop is moved with a constant velocity

\vec{v} = v_{0}\hat{i}

. The emf induced in the loop is :

(A) $\frac{B_{0}v_{0}^{2}d}{2a}$
(B) $\frac{B_{0}v_{0}d}{2a}$
(C) $\frac{B_{0}v_{0}d^{2}}{a}$
(D) $\frac{B_{0}v_{0}d^{2}}{2a}$

Q115·PhysicsSingle correctJEE Main 2021

An aeroplane, with its wings spread 10 m, is flying at a speed of 180 km/h in a horizontal direction. The total intensity of earth's field at that part is

2.5 \times 10^{-4}

Wb/m

^2

and the angle of dip is 60°. The emf induced between the tips of the plane wings will be __________.

(A)88.37 mV
(B)62.50 mV
(C)54.125 mV
(D)108.25 mV

Q116·PhysicsNumericalJEE Main 2021

A coil of inductance 2 H having negligible resistance is connected to a source of supply whose voltage is given by V =3t volt. (where t is in second). If the voltage is applied when t = 0, then the energy stored in the coil after 4 s is ________ J.

Q117·PhysicsSingle correctJEE Main 2021

The current (i) at time t=0 and

t = \infty

respectively for the given circuit is :

(A) $\dfrac{18E}{55}, \dfrac{5E}{18}$
(B) $\dfrac{5E}{18}, \dfrac{18E}{55}$
(C) $\dfrac{5E}{18}, \dfrac{10E}{33}$
(D) $\dfrac{10E}{33}, \dfrac{5E}{18}$

Q118·PhysicsSingle correctJEE Main 2021

Figure shows a circuit that contains four identical resistors with resistance R = 2.0

\Omega

. Two identical inductors with inductance L = 2.0 mH and an ideal battery with emf E = 9.V. The current 'i' just after the switch 's' is closed will be :

(A)9A
(B)3.0 A
(C)2.25 A
(D)3.37 A

Q119·PhysicsSingle correctJEE Advanced 2020

A light disc made of aluminium (a nonmagnetic material) is kept horizontally and is free to rotate about its axis as shown in the figure. A strong magnet is held vertically at a point above the disc away from its axis. On revolving the magnet about the axis of the disc, the disc will (figure is schematic and not drawn to scale)-

(A)rotate in the direction opposite to the direction of magnet's motion
(B)rotate in the same direction as the direction of magnet's motion
(C)not rotate and its temperature will remain unchanged
(D)not rotate but its temperature will slowly rise

Q120·PhysicsNumericalJEE Advanced 2020

The inductors of two

LR

circuits are placed next to each other, as shown in the figure. The values of the self-inductance of the inductors, resistances, mutual-inductance and applied voltages are specified in the given circuit. After both the switches are closed simultaneously, the total work done by the batteries against the induced

EMF

in the inductors by the time the currents reach their steady state values is_________ mJ.

Q121·PhysicsNumericalJEE Main 2020

A part of complete circuit is shown in the figure. At some instant, the value of current I is 1 A and it is decreasing at a rate of

10^2\text{As}^{-1}

. The value of the potential difference

V_P-V_Q

, (in volts) at that instant, is __________.

Q122·PhysicsNumericalJEE Main 2020

Two concentric circular coils, C

_1

and C

_2

are placed in the XY plane. C

_1

has 500 turns, and a radius of 1 cm. C

_2

has 200 turns and radius of 20 cm. C

_2

carries a time dependent current

I(t) = (5t^2 - 2t + 3)

A where t is in s. The emf induced in C

_1

(in mV), at the instant t = 1 s is

\dfrac{4}{x}

. The value of x is ________.

Q123·PhysicsSingle correctJEE Main 2020

A series L-R circuit is connected to a battery of emf V. If the circuit is switched on at t = 0, then the time at which the energy stored in the inductor reaches (1/n) times of its maximum value, is :

(A) $\frac{L}{R}\ln\left(\frac{\sqrt{n}}{\sqrt{n}+1}\right)$
(B) $\frac{L}{R}\ln\left(\frac{\sqrt{n}+1}{\sqrt{n}-1}\right)$
(C) $\frac{L}{R}\ln\left(\frac{\sqrt{n}-1}{\sqrt{n}}\right)$
(D) $\frac{L}{R}\ln\left(\frac{\sqrt{n}}{\sqrt{n}-1}\right)$

Q124·PhysicsSingle correctJEE Main 2020

A small bar magnet is moved through a coil at constant speed from one end to the other. Which of the following series of observations will be seen on the galvanometer G attached across the coil? Three positions shown describe: (a) the magnet's entry (b) magnet is completely inside and (c) magnet's exit

(A)(A)
(B)(B)
(C)(C)
(D)(D)

Q125·PhysicsSingle correctJEE Main 2020

An elliptical loop having resistance R, of semi major axis a and semi minor axis b is placed in a magnetic field as shown in the figure. If the loop is rotated about the x-axis with angular frequency ω, the average power loss in the loop due to joule heating is:

(A) $\frac{\pi^{2}a^{2}b^{2}B^{2}\omega^{2}}{R}$
(B)zero
(C) $\frac{\pi abB\omega}{R}$
(D) $\frac{\pi^{2}a^{2}b^{2}B^{2}\omega^{2}}{2R}$

Q126·PhysicsSingle correctJEE Main 2020

A uniform magnetic field B exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of 4 mm and a total length of 30 cm. The magnetic field changes with time at a steady rate

\frac{dB}{dt}=0.032\,Ts^{-1}

. The induced current in the loop is close to (Resistivity of the metal wire is

1.23\times 10^{-8}\,\Omega m

)

(A) $0.61A$
(B) $0.43\,A$
(C) $0.53\,A$
(D) $0.34\,A$

Q127·PhysicsNumericalJEE Main 2020

In a fluorescent lamp choke (a small transformer) 100 V of reverse voltage is produced when the choke current changes uniformly from 0.25 A to 0 in a duration of 0.025 ms. The self-inductance of the choke (in mH) is estimated to be ____.

Q128·PhysicsSingle correctJEE Main 2020

As shown in the figure, a battery of emf

\varepsilon

is connected to an inductor L and resistance R in series. The switch is closed at t = 0. The total charge that flows from the battery, between t = 0 and t = t

_{c}

(t

_{c}

is the time constant of the circuit) is

(A) $\dfrac{\varepsilon L}{eR^{2}}$
(B) $\dfrac{\varepsilon L}{R^{2}}\left(1-\dfrac{1}{e}\right)$
(C) $\dfrac{\varepsilon R}{eL^{2}}$
(D) $\dfrac{\varepsilon L}{R^{2}}$

Q129·PhysicsSingle correctJEE Main 2020

At time t = 0 magnetic field of 1000 Gauss is passing perpendicularly through the area defined by the closed loop shown in the figure. If the magnetic field reduces linearly to 500 Gauss, in the next 5s, then induced EMF in the loops is:

(A)28 $\mu$ V
(B)56 $\mu$ V
(C)48 $\mu$ V
(D)36 $\mu$ V

Q130·PhysicsSingle correctJEE Main 2020

A planar loop of wire rotates in a uniform magnetic field. Initially, at t = 0, the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of 10 s about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at:

(A)2.5 s and 5.0 s
(B)5.0 s and 10.0 s
(C)2.5 s and 7.5 s
(D)5.0 and 7.5 s

Q131·PhysicsSingle correctJEE Main 2020

A long solenoid of radius R carries a time (t) dependent current I (t) =

I_0 t (1-t)

. A ring of radius 2R is placed cordially near its middle. During the time internal

0 \le t \le 1

, the induced current (

I_R

) and the induced EMF (

V_R

) in the ring changes as:

(A)At t = 0.25 direction of $I_R$ reverses and $V_R$ is maximum.
(B)Direction of $I_R$ remains unchanged and $V_R$ is zero at t = 0.25
(C)Direction of $I_R$ remains unchanged and $V_R$ is maximum at t = 0.5
(D)At t = 0.5 direction of $I_R$ reverses and $V_R$ is zero.

Q132·PhysicsNumericalJEE Main 2020

A loop ABCDEFA of straight edges has six corner points A (0, 0, 0), B (5, 0, 0), C(5, 5, 0), D(0, 5, 0), E(0, 5, 5) and F(0, 0, 5). The magnetic field in this region in

\vec{B} = (3\hat{i} + 4\hat{k})

T. The quantity of flux through the loop ABCDEFA (in Wb) is _________.

Q133·PhysicsNumericalJEE Advanced 2019

A 10 cm long perfectly conducting wire PQ is moving with a velocity 1 cm/s on a pair of horizontal rails of zero resistance. One side of the rails is connected to an inductor L = 1 mH and a resistance R = 1

\Omega

as shown in the figure. The horizontal rails, L and R lie in the same plane with a uniform magnetic field B = 1 T perpendicular to the plane. If the key S is closed at certain instant, the current in the circuit after 1 millisecond is

x \times 10^{-3}

A, where the value of x is ________. [Assume the velocity of wire PQ remains constant (1 cm/s) after key S is closed. Given:

e^{-1} = 0.37

, where e is base of the natural logarithm]

Q134·PhysicsMultiple correctJEE Advanced 2019

A conducting wire of parabolic shape, initially

y = x^2

, is moving with velocity

\vec{V} = V_0\hat{i}

in a non uniform magnetic field

\vec{B} = B_0\left(1+\left(\frac{y}{L}\right)^{\beta}\right)\hat{k}

, as shown in figure. If

V_0

,

B_0

, L and β are positive constants and Δφ is the potential difference developed between the ends of the wire, then the correct statement(s) is/are:

(A) $|\Delta\phi|$ is proportional to the length of the wire projected on the y-axis.
(B) $|\Delta\phi|$ remains the same if the parabolic wire is replaced by a straight wire, y = x initially, of length $\sqrt{2}$ L
(C) $|\Delta\phi| = \frac{1}{2}B_0V_0L$ for β = 0
(D) $|\Delta\phi| = \frac{4}{3}B_0V_0L$ for β = 2

Q135·PhysicsSingle correctJEE Main 2019

The figure shows a square loop L of side 5 cm which is connected to a network of resistances. The whole set up is moving towards right with a constant speed of 1 cms

^{-1}

. At some instant, a part of L is in a uniform magnetic field of 1 T, perpendicular to the plane of the loop. If the resistance of L is 1.7 Ω, the current in the loop at that instant will be close to :

(A)115 μA
(B)170 μA
(C)60 μA
(D)150 μA

Q136·PhysicsSingle correctJEE Main 2019

Consider the LR circuit shown in the figure. If the switch S is closed at t = 0 then the amount of charge that passes through the battery between t = 0 and

t = \dfrac{L}{R}

is :

(A) $\dfrac{EL}{7.3R^{2}}$
(B) $\dfrac{EL}{2.7R^{2}}$
(C) $\dfrac{7.3EL}{R^{2}}$
(D) $\dfrac{2.7EL}{R^{2}}$

Q137·PhysicsSingle correctJEE Main 2019

A coil of self inductance 10 mH and resistance 0.1 Ω is connected through a switch to a battery of internal resistance 0.9 Ω. After the switch is closed the time taken for the current to attain 80% of the saturation values is: [take ln 5 = 1.6]

(A)0.016 s
(B)0.324 s
(C)0.002 s
(D)0.103 s

Q138·PhysicsSingle correctJEE Main 2019

Two coils P and Q are separated by some distance. When a current of 3 A flows through coil P a magnetic flux of

10^{-3}

Wb passes through Q. No current is passed through Q. When no current passes through P and a current of 2 A passes through Q, the flux through P is:

(A) $6.67 \times 10^{-3}$ Wb
(B) $6.67 \times 10^{-4}$ Wb
(C) $3.67 \times 10^{-4}$ Wb
(D) $3.67 \times 10^{-3}$ Wb

Q139·PhysicsSingle correctJEE Main 2019

The total number of turns and cross-section area in solenoid is fixed. However, its length L is varied by adjusting the separation between windings. The inductance of solenoid will be proportional to:

(A)1/L
(B)L
(C)1/L $^2$
(D)L $^2$

Q140·PhysicsSingle correctJEE Main 2019

A very long solenoid of radius R is carrying current

I(t) = kte^{-\alpha t}

(k > 0)

, as a function of time

(t \geq 0)

. counter clockwise current is taken to be positive. A circular conducting coil of radius 2R is placed in the equatorial plane of the solenoid and concentric with the solenoid. The current induced in the outer coil is correctly depicted, as a function of time, by:-

(A)(A)
(B)(B)
(C)(C)
(D)(D)

Q141·PhysicsSingle correctJEE Main 2019

A 20 Henry inductor coil is connected to a 10 ohm resistance in series as shown in figure. The time at which rate of dissipation of energy (Joule's heat) across resistance is equal to the rate at which magnetic energy is stored in the inductor, is

(A) $\dfrac{2}{\ln 2}$
(B) $\ln 2$
(C) $\dfrac{1}{2}\ln 2$
(D) $2\ln 2$

Q142·PhysicsSingle correctJEE Main 2019

A thin strip 10 cm long is on a U shaped wire of negligible resistance and it is connected to a spring of spring constant 0.5 N m

^{-1}

(see figure). The assembly is kept in a uniform magnetic field of 0.1 T. If the strip is pulled from its equilibrium position and released, the number of oscillations it performs before its amplitude decreases by a factor of e is N. If the mass of the strip is 50 grams, its resistance

10\,\Omega

and air drag negligible, N will be close to:

(A)50000
(B)10000
(C)1000
(D)5000

Q143·PhysicsSingle correctJEE Main 2019

A 10 m long horizontal wire extends from North East to South West. It is falling with a speed of 5.0 ms

^{-1}

, at right angles to the horizontal component of the earth's magnetic field, of

0.3\times10^{-4}

Wb/m

^{2}

. The value of the induced emf in wire is :

(A) $1.5\times10^{-3}$ V
(B) $1.1\times10^{-3}$ V
(C) $2.5\times10^{-3}$ V
(D) $0.3\times10^{-3}$ V

Q144·PhysicsSingle correctJEE Main 2019

In the figure shown, a circuit contains two identical resistors with resistance R = 5

\Omega

and an inductance with L = 2 mH. An ideal battery of 15 V is connected in the circuit. What will be the current through the battery long after the switch is closed?

(A)5.5 A
(B)7.5 A
(C)3 A
(D)6 A

Q145·PhysicsSingle correctJEE Main 2019

There are two long co – axial solenoids of same length l. The inner and outer coils have radii r

_1

and r

_2

and number of turns per unit length n

_1

and n

_2

respectively. The ratio of mutual inductance to the self – inductance of the inner – coil is:

(A) $\frac{n_1}{n_2}$
(B) $\frac{n_2}{n_1}\cdot\frac{r_1}{r_2}$
(C) $\frac{n_2}{n_1}\cdot\frac{r_2^2}{r_1^2}$
(D) $\frac{n_2}{n_1}$

Q146·PhysicsSingle correctJEE Main 2019

A copper wire is wound on a wooden frame, whose shape is that of an equilateral triangle. If the linear dimension of each side of the frame is increased by a factor of 3, keeping the number of turns of the coil per unit length of the frame the same, then self inductance of the coil:

(A)decreases by a factor of 9
(B)increases by a factor of 27
(C)increases by a factor of 3
(D)decreases by a factor of $9\sqrt{3}$

Q147·PhysicsSingle correctJEE Main 2019

A solid metal cube of edge length 2 cm is moving in a positive y-direction at a constant speed of 6 m/s. There is a uniform magnetic field of 0.1 T in the positive z-direction. The potential difference between the two faces of the cube perpendicular to the x-axis, is:

(A)12 mV
(B)6 mV
(C)1 mV
(D)2 mV

Q148·PhysicsMultiple correctJEE Advanced 2018

In the figure below, the switches

S_{1}

and

S_{2}

are closed simultaneously at

t = 0

and a current starts to flow in the circuit. Both the batteries have the same magnitude of the electromotive force (emf) and the polarities are as indicated in the figure. Ignore mutual inductance between the inductors. The current

I

in the middle wire reaches its maximum magnitude

I_{max}

at time

t = \tau

. Which of the following statements is (are) true?

(A) $I_{max} = \frac{V}{2R}$
(B) $I_{max} = \frac{V}{4R}$
(C) $\tau = \frac{L}{R}\ln 2$
(D) $\tau = \frac{2L}{R}\ln 2$

Q149·PhysicsMultiple correctJEE Advanced 2017

A circular insulated copper wire loop is twisted to form two loops of area A and 2A as shown in the figure. At the point of crossing the wires remain electrically insulated from each other. The entire loop lies in the plane (of the paper). A uniform magnetic field

\vec{B}

points into the plane of the paper. A uniform magnetic field

\vec{B}

points into the plane of the paper. At t = 0, the loop starts rotating about the common diameter as axis with a constant angular velocity

\omega

in the magnetic field. Which of the following options is/are correct?

(A)The rate of change of the flux is maximum when the plane of the loops is perpendicular to plane of the paper.
(B)The net emf induced due to both the loops is proportional to cos $\omega t$ .
(C)The emf induced in the loop is proportional to the sun of the areas of the two loops.
(D)The amplitude of the maximum net emf induced due to both the loops is equal to the amplitude of maximum emf induced in the smaller loop alone.

Q150·PhysicsMultiple correctJEE Advanced 2017

A source of constant voltage V is connected to a resistance R and two ideal inductors

L_{1}

and

L_{2}

through a switch S as shown. There is no mutual inductance between the two inductors. The switch S is initially open. At

t = 0

, the switch is closed and current begins to flow. Which of the following options is/are correct?

(A)After a long time, the current through $L_{1}$ will be $\dfrac{V}{R}\dfrac{L_{2}}{L_{1}+L_{2}}$
(B)After a long time, the current through $L_{2}$ will be $\dfrac{V}{R}\dfrac{L_{1}}{L_{1}+L_{2}}$
(C)The ratio of the currents through $L_{1}$ and $L_{2}$ is fixed at all times $(t > 0)$
(D)At $t = 0$ , the current through the resistance R is $\dfrac{V}{R}$

Q151·PhysicsMultiple correctJEE Advanced 2016

A conducting loop in the shape of a right angled isosceles triangle of height 10 cm is kept such that the

90°

vertex is very close to an infinitely long conducting wire (see the figure). The wire is electrically insulated from the loop. The hypotenuse of the triangle is parallel to the wire. The current in the triangular loop is in counterclockwise direction and increased at a constant rate of

10\ \text{A s}^{-1}

. Which of the following statement(s) is(are) true?

(A)The magnitude of induced $emf$ in the wire is $\left(\frac{\mu_0}{\pi}\right)$ volt
(B)If the loop is rotated at a constant angular speed about the wire, an additional $emf$ of $\left(\frac{\mu_0}{\pi}\right)$ volt is induced in the wire
(C)The induced current in the wire is in opposite direction to the current along the hypotenuse
(D)There is a repulsive force between the wire and the loop

Q152·PhysicsMultiple correctJEE Advanced 2016

A rigid wire loop of square shape having side of length L and resistance R is moving along the x-axis with a constant velocity

v_{0}

in the plane of the paper. At t = 0, the right edge of the loop enters a region of length 3L where there is a uniform magnetic field

B_{0}

into the plane of the paper, as shown in the figure. For sufficiently large

v_{0}

, the loop eventually crosses the region. Let x be the location of the right edge of the loop. Let v(x), I(x) and F(x) represent the velocity of the loop, current in the loop, and force on the loop, respectively, as a function of x. Counter-clockwise current is taken as positive. Which of the following schematic plot(s) is(are) correct? (Ignore gravity)

(A)(A)
(B)(B)
(C)(C)
(D)(D)

Q153·PhysicsIntegerJEE Advanced 2016

Two inductors

L_1

(inductance 1 mH, internal resistance 3Ω) and

L_2

(inductance 2 mH, internal resistance 4Ω), and a resistor R (resistance 12Ω) are all connected in parallel across a 5V battery. The circuit is switched on at time

t = 0

. The ratio of the maximum to the minimum current (

I_{max} / I_{min}

) drawn from the battery is

Q154·PhysicsSingle correctJEE Advanced 2013

A point Q is moving in a circular orbit of radius

R

in the x-y plane with an angular velocity

\omega

. This can be considered as equivalent to a loop carrying a steady current

\frac{Q\omega}{2\pi}

. A uniform magnetic field along the positive z-axis is now switched on, which increases at a constant rate from

0

to

B

in one second. Assume that the radius of the orbit remains constant. The application of the magnetic field induces an emf in the orbit. The induced emf is defined as the work done by an induced electric field in moving a unit positive charge around closed loop. It is known that, for an orbiting charge, the magnetic dipole moment is proportional to the angular momentum with a proportionality constant

\gamma

. The change in the magnetic dipole moment associated with the orbit, at the end of time interval of the magnetic field change, is

(A) $-\gamma BQR^{2}$
(B) $-\gamma\frac{BQR^{2}}{2}$
(C) $\gamma\frac{BQR^{2}}{2}$
(D) $\gamma BQR^{2}$

Q155·PhysicsSingle correctJEE Advanced 2013

A point Q is moving in a circular orbit of radius

R

in the x-y plane with an angular velocity

\omega

. This can be considered as equivalent to a loop carrying a steady current

\frac{Q\omega}{2\pi}

. A uniform magnetic field along the positive z-axis is now switched on, which increases at a constant rate from

0

to

B

in one second. Assume that the radius of the orbit remains constant. The application of the magnetic field induces an emf in the orbit. The induced emf is defined as the work done by an induced electric field in moving a unit positive charge around closed loop. It is known that, for an orbiting charge, the magnetic dipole moment is proportional to the angular momentum with a proportionality constant

\gamma

. The magnitude of the induced electric field in the orbit at any instant of time during the time interval of the magnetic field change, is

(A) $\frac{BR}{4}$
(B) $\frac{BR}{2}$
(C) $BR$
(D) $2BR$

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