How many questions from Electric Potential appear in JEE?

Electric Potential has appeared in 63 of the last 186 JEE Main and JEE Advanced papers — about 34% of them — contributing 70 questions in total across those papers.

Is Electric Potential an important chapter for JEE?

Judged by how often it is actually tested, it appears in roughly 34% 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 Electric Potential 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.

Electric Potential JEE Previous Year Questions with Answers

Q1·PhysicsMultiple correctJEE Advanced 2026

Two charges

Q_{1} = q

and

Q_{2} = mq

are placed at the points

P_{1}(a, b)

and

P_{2}(ma, mb)

, respectively, in the

XY

plane, where

a, b \neq 0

and

m \neq 0, 1

. If

V_{1}

is the potential at a point in the

XY

plane due to charge

Q_{1}

and

V_{2}

is the potential at that point due to charge

Q_{2}

. Correct statement(s) for the points at which

|V_{1}| = |V_{2}|

is/are:

(A)For $m = -1$ , locus of these points is $ax + by = 0$ .
(B)For $m = 2$ , the locus of these points is a circle of radius $\frac{2}{3}\sqrt{a^{2} + b^{2}}$ centered at $\left(\frac{2}{3}a, \frac{2}{3}b\right)$
(C)For $m = -2$ , the locus of these points is a circle of radius $2\sqrt{a^{2} + b^{2}}$ centered at $(2a, 2b)$
(D)For $m = -3$ , locus of these points is $3bx + 3ay = 0$ .

Q2·PhysicsNumericalJEE Main 2026

A three coulomb charge moves from the point

(0, -2, -5)

to the point

(5, 1, 2)

in an electric field expressed as

\vec{E} = 2x\hat{i} + 3y^{2}\hat{j} + 4\hat{k}

N/C. The work done in moving the charge is _______ J.

Q3·PhysicsSingle correctJEE Main 2026

The electric potential as a function of

x, y

is given by

V = 5(x^{2} - y^{2})

V. The electric field at a point

(2, 3)

m is __________ V/m.

(A) $(-20\hat{i} + 30\hat{j})$
(B) $(20\hat{i} - 30\hat{j})$
(C) $(20\hat{i} + 45\hat{j})$
(D) $(-4\hat{i} + 6\hat{j})$

Q4·PhysicsSingle correctJEE Main 2026

Two metal plates

(A, B)

are kept horizontally with separation of

\left(\frac{12}{\pi}\right)

cm, with plate A on the top. An atomizer jet sprays oil (density 1.5 g/cm

^{3}

) droplets of radius 1 mm horizontally. All oil droplets carry a charge 5 nC. The potentials

V_A

and

V_B

are required on plates A and B respectively in order to ensure the droplets do not descend. The values of

V_A

and

V_B

are ________. (Neglect the air resistance to the droplets and take

g = 10

m/s

^{2}

)

(A) $100\,V$ and $580\,V$
(B) $580\,V$ and $100\,V$
(C) $60\,V$ and $400\,V$
(D) $0\,V$ and $-200\,V$

Q5·PhysicsSingle correctJEE Main 2026

Two charged conducting spheres

S_{1}

and

S_{2}

of radii 8 cm and 18 cm are connected to each other by a wire. After equilibrium is established, the ratio of electric fields on

S_{1}

and

S_{2}

spheres are

E_{S_{1}}

and

E_{S_{2}}

respectively. The value of

\frac{E_{S_{1}}}{E_{S_{2}}}

is ______.

(A) $\frac{3}{2}$
(B) $\frac{2}{3}$
(C) $\frac{4}{9}$
(D) $\frac{9}{4}$

Q6·PhysicsSingle correctJEE Main 2026

Which one of the following is not a measurable quantity ?

(A)Voltage difference
(B)Resistance
(C)Voltage
(D)Displacement current

Q7·PhysicsSingle correctJEE Main 2026

Two point charges of 1 nC and 2 nC are placed at the two corners of equilateral triangle of side 3 cm. The work done in bringing a charge of 3 nC from infinity to the third corner of the triangle is _______ μJ.

\frac{1}{4\pi \in_{0}} = 9 \times 10^{9}\,\text{N.m}^{2} / \text{C}^{2}

(A)2.7
(B)5.4
(C)3.3
(D)27

Q8·PhysicsSingle correctJEE Main 2026

There are three co-centric conducting spherical shells A, B and C of radii a, b and c respectively. The potential of the spheres A, B and C respectively, are :

(A) $\frac{1}{4\pi \in_{0}}\left(\frac{q_{1}+q_{2}+q_{3}}{a}\right), \frac{1}{4\pi \in_{0}}\left(\frac{q_{1}+q_{2}+q_{3}}{b}\right), \frac{1}{4\pi \in_{0}}\left(\frac{q_{1}+q_{2}+q_{3}}{c}\right)$
(B) $\frac{1}{4\pi \in_{0}}\left(\frac{q_{1}+q_{2}+q_{3}}{a}\right), \frac{1}{4\pi \in_{0}}\left(\frac{q_{1}+q_{2}}{b}+\frac{q_{3}}{c}\right), \frac{1}{4\pi \in_{0}}\left(\frac{q_{1}}{a}+\frac{q_{2}}{b}+\frac{q_{3}}{c}\right)$
(C) $\frac{1}{4\pi \in_{0}}\left(\frac{q_{1}}{a}+\frac{q_{2}}{b}+\frac{q_{3}}{c}\right), \frac{1}{4\pi \in_{0}}\left(\frac{q_{1}+q_{2}}{b}+\frac{q_{3}}{c}\right), \frac{1}{4\pi \in_{0}}\left(\frac{q_{1}+q_{2}+q_{3}}{c}\right)$
(D) $\frac{1}{4\pi \in_{0}}\left(\frac{q_{1}}{a}+\frac{q_{2}}{b}+\frac{q_{3}}{c}\right), \frac{1}{4\pi \in_{0}}\left(\frac{q_{1}+q_{2}+q_{3}}{b}\right), \frac{1}{4\pi \in_{0}}\left(\frac{q_{1}+q_{2}+q_{3}}{c}\right)$

Q9·PhysicsSingle correctJEE Main 2026

Two charges 7μC and −2 μC are placed at (−9, 0, 0) cm and (9, 0, 0) cm respectively in an external field

E = \frac{A}{r^{2}}\hat{r}

, where

A = 9 \times 10^{5}

N/C.m

^{2}

. Considering the potential at infinity is 0, the electrostatic energy of the configuration is_____J.

(A)1.4
(B)−90.7
(C)49.3
(D)24.3

Q10·PhysicsSingle correctJEE Main 2026

Electric field in a region is given by

\vec{E} = Ax\hat{i} + By\hat{j}

, where

A

= 10 V/m

^2

and

B

= 5 V/m

^2

. If the electric potential at a point (10, 20) is 500 V, then the electric potential at origin is ______ V.

(A)1000
(B)500
(C)2000
(D)0

Q11·PhysicsSingle correctJEE Main 2026

Three small identical bubbles of water having same charge on each coalesce to form a bigger bubble. Then the ratio of the potentials on one initial bubble and that on the resultant bigger bubble is :

(A)1 : 3 $^{1/3}$
(B)1 : 2 $^{2/3}$
(C)3 $^{2/3}$ : 1
(D)1 : 3 $^{2/3}$

Q12·PhysicsSingle correctJEE Main 2026

A point charge of

10^{-8}

C is placed at origin. The work done in moving a point charge 2 μC from point A(4, 4, 2) m to B(2, 2, 1) m is ___________J.

(\frac{1}{4\pi \in_0} = 9 \times 10^{9}

in SI units)

(A) $45 \times 10^{-6}$
(B)0
(C) $30 \times 10^{-6}$
(D) $15 \times 10^{-6}$

Q13·PhysicsSingle correctJEE Main 2026

Consider two identical metallic spheres of radius

R

each having charge

Q

and mass

m

. Their centers have an initial separation of

4R

. Both the spheres are given an initial speed of

u

towards each other. The minimum value of u, so that they can just touch each other is : (Take

k = \frac{1}{4\pi \in_0}

and assume

kQ^2 > Gm^2

where G is the Gravitational constant)

(A) $\sqrt{\frac{kQ^2}{4mR}\left(1 - \frac{Gm^2}{kQ^2}\right)}$
(B) $\sqrt{\frac{kQ^2}{4mR}\left(1 + \frac{Gm^2}{kQ^2}\right)}$
(C) $\sqrt{\frac{kQ^2}{2mR}\left(1 - \frac{Gm^2}{kQ^2}\right)}$
(D) $\sqrt{\frac{kQ^2}{2mR}\left(1 - \frac{Gm^2}{2kQ^2}\right)}$

Q14·PhysicsMultiple correctJEE Advanced 2025

A positive point charge of

10^{-8}

C is kept at a distance of 20 cm from the center of a neutral conducting sphere of radius 10 cm. The sphere is then grounded and the charge on the sphere is measured. The grounding is then removed and subsequently the point charge is moved by a distance of 10 cm further away from the center of the sphere along the radial direction. Taking

\frac{1}{4\pi\varepsilon_0} = 9\times 10^9

Nm

^2

/C

^2

(where

\varepsilon_0

is the permittivity of free space), which of the following statements is/are correct:

(A)Before the grounding, the electrostatic potential of the sphere is 450 V .
(B)Charge flowing from the sphere to the ground because of grounding is $5\times 10^{-9}$ C.
(C)After the grounding is removed, the charge on the sphere is $-5\times 10^{-9}$ C.
(D)The final electrostatic potential of the sphere is 300 V.

Q15·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: Work done in moving a test charge between two points inside a uniformly charged spherical shell is zero, no matter which path is chosen. Reason R: Electrostatic potential inside a uniformly charged spherical shell is constant and is same as that on the surface of the shell. In the light of the above statements, choose the correct answer from the options given below:

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

Q16·PhysicsSingle correctJEE Main 2025

Two charges

q_1

and

q_2

are separated by a distance of 30 cm. A third charge

q_3

initially at C as shown in the figure, is moved along the circular path of radius 40 cm from C to D. If the difference in potential energy due to movement of

q_3

from C to D is given by

\dfrac{q_3K}{4\pi\varepsilon_0}

, the value of K is:

(A) $8q_2$
(B) $6q_2$
(C) $8q_1$
(D) $6q_1$

Q17·PhysicsSingle correctJEE Main 2025

The electrostatic potential on the surface of a uniformly charged spherical shell of radius

R=10

cm is 120 V. The potential at the centre of the shell, at a distance

r=5

cm from the centre, and at a distance

r=15

cm from the centre of the shell respectively, are:

(A)120V, 120V, 80V
(B)40V, 40V, 80V
(C)0V, 0V, 80V
(D)0V, 120V, 40V

Q18·PhysicsSingle correctJEE Main 2025

Two large plane parallel conducting plates are kept 10 cm apart as shown in the figure. The potential difference between them is V. The potential difference between the points A and B (shown in the figure) is:

(A) $\dfrac{1}{4}V$
(B) $\dfrac{2}{5}V$
(C) $\dfrac{3}{4}V$
(D) $1\,V$

Q19·PhysicsSingle correctJEE Main 2025

Three infinitely long wires with linear charge density

\lambda

are placed along the x-axis, y-axis and z-axis respectively. Which of the following denotes an equipotential surface?

(A) $xy+yz+zx=$ constant
(B) $(x+y)(y+z)(z+x)=$ constant
(C) $(x^2+y^2)(y^2+z^2)(z^2+x^2)=$ constant
(D) $xyz=$ constant

Q20·PhysicsSingle correctJEE Main 2025

In the first configuration (1) as shown in the figure, four identical charges

(q_0)

are kept at the corners A, B, C and D of a square of side length "a". In the second configuration (2), the same charges are shifted to mid points G, E, F and H, of the sides of the square. If

K=\dfrac{1}{4\pi\varepsilon_0}

, the difference between the potential energy of configuration (2) and (1) is given by:

(A) $\dfrac{Kq_0^2}{a}\left(4\sqrt2-2\right)$
(B) $\dfrac{Kq_0^2}{a}\left(3-\sqrt2\right)$
(C) $\dfrac{Kq_0^2}{a}\left(4-2\sqrt2\right)$
(D) $\dfrac{Kq_0^2}{a}\left(3\sqrt2-2\right)$

Q21·PhysicsSingle correctJEE Main 2025

Two charges

7\,\mu c

and

-4\,\mu c

are placed at

(-7\text{ cm}, 0, 0)

and

(7\text{ cm}, 0, 0)

respectively. Given,

\varepsilon_0=8.85\times10^{-12}\ \mathrm{C^2\,N^{-1}\,m^{-2}}

, the electrostatic potential energy of the charge configuration is :

(A) $-1.5$ J
(B) $-2.0$ J
(C) $-1.2$ J
(D) $-1.8$ J

Q22·PhysicsNumericalJEE Advanced 2024

An infinitely long thin wire, having a uniform charge density per unit length of 5nC/m, is passing through a spherical shell of radius 1m, as shown in the figure. A 10nC charge is distributed uniformly over the spherical shell. If the configuration of the charges remains static, the magnitude of the potential difference between points P and R, in Volt, is [Given: In SI units

\frac{1}{4\pi\varepsilon_0}

= 9 ×

10^9

, ln 2 = 0.7. Ignore the area pierced by the wire.]

Q23·PhysicsSingle correctJEE Main 2024

Two charged conducting spheres of radii

a

and

b

are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:

(A) $\sqrt{ab}$
(B) $ab$
(C) $\dfrac{a}{b}$
(D) $\dfrac{b}{a}$

Q24·PhysicsNumericalJEE Main 2024

The distance between charges

+q

and

-q

is

2\ell

and between

+2q

and

-2q

is

4\ell

. The electrostatic potential at point P at a distance

r

from centre O is

-\alpha\dfrac{q\ell}{r^2}\times10^9

V, where the value of

\alpha

is ______. (Use

\dfrac{1}{4\pi\varepsilon_0}=9\times10^9

Nm

^2

C

^{-2}

)

Q25·PhysicsSingle correctJEE Main 2024

The electrostatic potential due to an electric dipole at a distance

r

varies as:

(A) $r$
(B) $\dfrac{1}{r^2}$
(C) $\dfrac{1}{r^3}$
(D) $\dfrac{1}{r}$

Q26·PhysicsSingle correctJEE Main 2024

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Work done by electric field on moving a positive charge on an equipotential surface is always zero. Reason (R) : Electric lines of forces are always perpendicular to equipotential surfaces. In the light of the above statements, choose the most appropriate answer from the options given below :

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

Q27·PhysicsNumericalJEE Main 2024

The electric potential at the surface of an atomic nucleus

(Z=50)

of radius

9\times10^{-13}

cm is ________

\times10^6

V.

Q28·PhysicsSingle correctJEE Main 2024

An electric charge

10^{-6}\,\mu

C is placed at origin (0, 0) m of X–Y co-ordinate system. Two points P and Q are situated at

(\sqrt3,\sqrt3)

m and

(\sqrt6,0)

m respectively. The potential difference between the points P and Q will be:

(A) $\sqrt3$ V
(B) $\sqrt6$ V
(C)0 V
(D)3 V

Q29·PhysicsSingle correctJEE Advanced 2023

An electric dipole is formed by two charges +q and - q located in xy-plane at (0, 2) mm and (0, -2) mm, respectively, as shown in the figure. The electric potential at point P (100, 100) mm due to the dipole is

V_0

. The charges +q and -q are then moved to the points (-1, 2) mm and (1, -2) mm, respectively. What is the value of electric potential at P due to the new dipole?

(A) $V_0/4$
(B) $V_0/2$
(C) $V_0 / \sqrt{2}$
(D) $3V_0/4$

Q30·PhysicsNumericalJEE Main 2023

64 identical drops each charged upto potential of 10 mV are combined to form a bigger drop. The potential of the bigger drop will be _________ mV.

Q31·PhysicsNumericalJEE Main 2023

Three concentric spherical metallic shells X, Y and Z of radius a, b and c respectively

[a<b<c]

have surface charge densities

\sigma, -\sigma

and

\sigma

respectively. The shells X and Z are at same potential. If the radii of X and Y are 2 cm and 3 cm respectively, the radius of shell Z is _________ cm.

Q32·PhysicsSingle correctJEE Main 2023

Electric potential at a point P due to a point charge of

5\times10^{-9}

C is 50 V. The distance of P from the point charge is: (Assume

\dfrac{1}{4\pi\varepsilon_0}=9\times10^{9}

Nm

^2

C

^{-2}

)

(A)3 cm
(B)9 cm
(C)90 cm
(D)0.9 cm

Q33·PhysicsSingle correctJEE Main 2023

For a uniformly charged thin spherical shell, the electric potential

(V)

radially away from the centre

(O)

of shell can be graphically represented as:

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

Q34·PhysicsSingle correctJEE Main 2023

Which of the following correctly represents the variation of electric potential (

V

) of a charged spherical conductor of radius (

R

) with radial distance (

r

) from the center?

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

Q35·PhysicsSingle correctJEE Main 2023

Two isolated metallic solid spheres of radii

R

and

2R

are charged such that both have same charge density

\sigma

. The spheres are then connected by a thin conducting wire. If the new charge density of the bigger sphere is

\sigma'

, the ratio

\dfrac{\sigma'}{\sigma}

is:

(A) $\dfrac43$
(B) $\dfrac53$
(C) $\dfrac56$
(D) $\dfrac94$

Q36·PhysicsSingle correctJEE Main 2023

A point charge

2\times10^{-2}\,C

is moved from

P

to

S

in a uniform electric field of

30\,NC^{-1}

directed along positive x-axis. If coordinates of

P

and

S

are

(1,2,0)

and

(0,0,0)

respectively, the work done by electric field will be:

(A) $1200\,mJ$
(B) $-1200\,mJ$
(C) $-600\,mJ$
(D) $600\,mJ$

Q37·PhysicsSingle correctJEE Main 2023

The electric potential at the centre of two concentric half rings of radii

R_1

and

R_2

, having same linear charge density

\lambda

is:

(A) $\dfrac{\lambda}{2\varepsilon_0}$
(B) $\dfrac{\lambda}{4\varepsilon_0}$
(C) $\dfrac{2\lambda}{\varepsilon_0}$
(D) $\dfrac{\lambda}{\varepsilon_0}$

Q38·PhysicsMultiple correctJEE Advanced 2022

A disk of radius R with uniform positive charge density

\sigma

is placed on the xy plane with its centre at the origin. The Coulomb potential along the z-axis is

V(z) = \frac{\sigma}{2\,\epsilon_0}\left(\sqrt{R^2 + z^2} - z\right).

A particle of positive charge q is placed initially at rest at a point on the z axis with

z = z_0

and

z_0 > 0

. In addition to the Coulomb force, the particle experiences a vertical force

\vec{F} = -c\hat{k}

with

c > 0

. Let

\beta = \frac{2c\,\epsilon_0}{q\sigma}

. Which of the following statements(s) is (are) correct?

(A)For $\beta = \frac{1}{4}$ and $z_0 = \frac{25}{7}R$ , the particle reaches the origin.
(B)For $\beta = \frac{1}{4}$ and $z_0 = \frac{3}{7}R$ , the particle reaches the origin.
(C)For $\beta = \frac{1}{4}$ and $z_0 = \frac{R}{\sqrt{3}}$ , the particle returns back to $z = z_0$ .
(D)For $\beta > 1$ and $z_0 > 0$ , the particle always reaches the origin.

Q39·PhysicsSingle correctJEE Main 2022

Given below are two statements. Statement I : Electric potential is constant within and at the surface of each conductor. Statement II : Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point. In the light of the above statements, choose the most appropriate answer from the options give below.

(A)Both statement I and statement II are correct
(B)Both statement I and statement II are incorrect
(C)Statement I is correct but statement II is incorrect
(D)Statement I is incorrect but and statement II is correct

Q40·PhysicsSingle correctJEE Main 2022

Two uniformly charged spherical conductors A and B of radii 5 mm and 10 mm are separated by a distance of 2 cm. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitudes of the electric fields at the surface of the sphere A and B will be :

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

Q41·PhysicsSingle correctJEE Main 2022

If the electric potential at any point (x, y, z)m in space is given by

V = 3x^2

volt. The electric field at the point (1, 0, 3) m will be :

(A)3 Vm $^{-1}$ , directed along positive x-axis.
(B)3 Vm $^{-1}$ , directed along negative x-axis.
(C)6 Vm $^{-1}$ , directed along positive x-axis.
(D)6 Vm $^{-1}$ , directed along negative x-axis.

Q42·PhysicsNumericalJEE Main 2022

27 identical drops are charged at 22V each. They combine to form a bigger drop. The potential of the bigger drop will be _____ V.

Q43·PhysicsNumericalJEE Advanced 2021

Two point charges

-Q

and

+Q/\sqrt{3}

are placed in the xy-plane at the origin (0, 0) and a point (2, 0), respectively, as shown in the figure. This results in an equipotential circle of radius

R

and potential V = 0 in the xy-plane with its center at

(b, 0)

. All lengths are measured in meters. The value of

b

is ______ meter.

Q44·PhysicsNumericalJEE Advanced 2021

Two point charges

-Q

and

+Q/\sqrt{3}

are placed in the xy-plane at the origin (0, 0) and a point (2, 0), respectively, as shown in the figure. This results in an equipotential circle of radius

R

and potential V = 0 in the xy-plane with its center at

(b, 0)

. All lengths are measured in meters. The value of

R

is ______ meter.

Q45·PhysicsSingle correctJEE Main 2021

The two thin coaxial rings, each of radius 'a' and having charges +Q and –Q respectively are separated by a distance of 's'. The potential difference between the centres of the two rings is :

(A) $\frac{Q}{2\pi\varepsilon_{0}}\left[\frac{1}{a} + \frac{1}{\sqrt{s^{2} + a^{2}}}\right]$
(B) $\frac{Q}{4\pi\varepsilon_{0}}\left[\frac{1}{a} + \frac{1}{\sqrt{s^{2} + a^{2}}}\right]$
(C) $\frac{Q}{4\pi\varepsilon_{0}}\left[\frac{1}{a} - \frac{1}{\sqrt{s^{2} + a^{2}}}\right]$
(D) $\frac{Q}{2\pi\varepsilon_{0}}\left[\frac{1}{a} - \frac{1}{\sqrt{s^{2} + a^{2}}}\right]$

Q46·PhysicsNumericalJEE Main 2021

27 similar drops of mercury are maintained at 10 V each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is ___________________ times that of a smaller drop.

Q47·PhysicsNumericalJEE Main 2021

512 identical drops of mercury are charged to a potential of 2 V each. The drops are joined to form a single drop. The potential of this drop is _____ V.

Q48·PhysicsIntegerJEE Advanced 2020

A point charge q of mass m is suspended vertically by a string of length

l

. A point dipole of dipole moment

\vec{p}

is now brought towards q from infinity so that the charge moves away. The final equilibrium position of the system including the direction of the dipole, the angles and distances is shown in the figure below. If the work done in bringing the dipole to this position is

N \times (mgh)

, where g is the acceleration due to gravity, then the value of

N

is _________. (Note that for three coplanar forces keeping a point mass in equilibrium,

\frac{F}{\sin\theta}

is the same for all forces, where F is any one of the forces and

\theta

is the angle between the other two forces)

Q49·PhysicsSingle correctJEE Main 2020

Two identical electric point dipoles have dipole moments

\vec{p}_{1} = p\hat{i}

and

\vec{p}_{2} = -p\hat{i}

and are held on the x axis at distance 'a' from each other. When released, they move along the x-axis with the direction of their dipole moments remaining unchanged. If the mass of each dipole is 'm', their speed when they are infinitely far apart is:

(A) $\frac{p}{a}\sqrt{\frac{1}{\pi ∈_{0} ma}}$
(B) $\frac{p}{a}\sqrt{\frac{1}{2\pi ∈_{0} ma}}$
(C) $\frac{p}{a}\sqrt{\frac{2}{\pi ∈_{0} ma}}$
(D) $\frac{p}{a}\sqrt{\frac{3}{2\pi ∈_{0} ma}}$

Q50·PhysicsSingle correctJEE Main 2020

Ten charges are placed on the circumference of a circle of radius R with constant angular separation between successive charges. Alternate charges 1, 3, 5, 7, 9 have charge (+ q) each, while 2, 4, 6, 8, 10 have charge (− q) each. The potential V and the electric field E at the centre of the circle are respectively: (Take V = 0 at infinity)

(A) $V = \dfrac{10q}{4\pi \epsilon_0 R}$ ; $E = \dfrac{10q}{4\pi \epsilon_0 R^{2}}$
(B) $V = 0$ ; $E = \dfrac{10q}{4\pi \epsilon_0 R^{2}}$
(C) $V = 0$ ; $E = 0$
(D) $V = \dfrac{10q}{4\pi \epsilon_0 R}$ ; $E = 0$

Q51·PhysicsSingle correctJEE Main 2020

A two point charges 4q and −q are fixed on the x-axis at

x = -\frac{d}{2}

and

x = \frac{d}{2}

, respectively. If a third point charge 'q' is taken from the origin to x = d along the semicircle as shown in the figure, the energy of the charge will:

(A)decrease by $\frac{4q^{2}}{3\pi \epsilon_{0} d}$
(B)increase by $\frac{2q^{2}}{3\pi \epsilon_{0} d}$
(C)increase by $\frac{3q^{2}}{4\pi \epsilon_{0} d}$
(D)decrease by $\frac{q^{2}}{4\pi \epsilon_{0} d}$

Q52·PhysicsSingle correctJEE Main 2020

Hydrogen ion and singly ionized helium atom are accelerated, from rest, through the same potential difference. The ratio of final speeds of hydrogen and helium ions is close to:

(A)1 : 2
(B)10 : 7
(C)5 : 7
(D)2 : 1

Q53·PhysicsSingle correctJEE Main 2020

Two isolated conducting spheres

S_1

and

S_2

of radius

\dfrac{2}{3}R

and

\dfrac{1}{3}R

have 12 μC and −3 μC charges, respectively, and are at a large distance from each other. They are now connected by a conducting wire. A long time after this is done the charges on

S_1

and

S_2

are respectively:

(A)+4.5 μC and −4.5 μC
(B)4.5 μC on both
(C)6 μC and 3 μC
(D)3 μC and 6 μC

Q54·PhysicsSingle correctJEE Main 2020

Concentric metallic hollow spheres of radii R and 4R hold charges

Q_1

and

Q_2

respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference V (R) − V (4R) is:

(A) $\dfrac{3Q_2}{4\pi \epsilon_0 R}$
(B) $\dfrac{Q_2}{4\pi \epsilon_0 R}$
(C) $\dfrac{3Q_1}{16\pi \epsilon_0 R}$
(D) $\dfrac{3Q_1}{4\pi \epsilon_0 R}$

Q55·PhysicsSingle correctJEE Main 2020

Consider two charged metallic spheres S

_{1}

and S

_{2}

of radii R

_{1}

and R

_{2}

, respectively. The electric fields E

_{1}

(on S

_{1}

) and E

_{2}

(on S

_{2}

) on their surfaces are such that E

_{1}

/E

_{2}

= R

_{1}

/R

_{2}

. Then the ratio of V

_{1}

(on S

_{1}

) / V

_{2}

(on S

_{2}

) of the electrostatic potentials on each sphere is:

(A) $(R_{1}/R_{2})^{2}$
(B) $\left(\dfrac{R_{1}}{R_{2}}\right)^{3}$
(C) $(R_{2}/R_{1})$
(D) $R_{1}/R_{2}$

Q56·PhysicsMultiple correctJEE Advanced 2019

An electric dipole with dipole moment

\frac{p_0}{\sqrt{2}}\left(\hat{i}+\hat{j}\right)

is held fixed at the origin O in the presence of an uniform electric field of magnitude

E_0

. If the potential is constant on a circle of radius R centered at the origin as shown in figure, then the correct statement(s) is/are : (

\epsilon_0

is permittivity of free space. R >> dipole size)

(A)Total electric field at point A is $\vec{E}_A = \sqrt{2}E_0\left(\hat{i}+\hat{j}\right)$
(B)Total electric field at point B is $\vec{E}_B = 0$
(C) $R = \left(\frac{p_0}{4\pi\epsilon_0 E_0}\right)^{1/3}$
(D)The magnitude of total electric field on any two points of the circle will be same.

Q57·PhysicsSingle correctJEE Advanced 2019

A thin spherical insulating shell of radius R carries a uniformly distributed charge such that the potential at its surface is

V_0

. A hole with a small area

\alpha 4\pi R^2 (\alpha << 1)

is made on the shell without affecting the rest of the shell. Which one of the following statements is correct?

(A)The magnitude of electric field at a point, located on a line passing through the hole and shell's center, on a distance 2R from the center of the spherical shell will be reduced by $\frac{\alpha V_0}{2R}$
(B)The magnitude of electric field at the center of the shell is reduced by $\frac{\alpha V_0}{2R}$
(C)The ratio of the potential at the center of the shell to that of the point at $\frac{1}{2}$ R from center towards the hole will be $\frac{1-\alpha}{1-2\alpha}$
(D)The potential at the center of the shell is reduced by $2\alpha V_0$

Q58·PhysicsSingle correctJEE Main 2019

A point dipole

\vec{p} = -p_0\hat{x}

is kept at the origin. The potential and electric field due to this dipole on the y-axis at a distance d are, respectively : (Take V = 0 at infinity)

(A) $\dfrac{|\vec{p}|}{4\pi\varepsilon_0 d^{2}}, \dfrac{-\vec{p}}{4\pi\varepsilon_0 d^{3}}$
(B) $0, \dfrac{\vec{p}}{4\pi\varepsilon_0 d^{3}}$
(C) $\dfrac{|\vec{p}|}{4\pi\varepsilon_0 d^{2}}, \dfrac{\vec{p}}{4\pi\varepsilon_0 d^{3}}$
(D) $0, \dfrac{-\vec{p}}{4\pi\varepsilon_0 d^{3}}$

Q59·PhysicsSingle correctJEE Main 2019

A uniformly charged ring of radius 3a and total charge q is placed in xy-plane centered at origin. A point charge q is moving towards the ring along the z-axis and has speed v at z = 4a. The minimum value of v such that it crosses the origin is:

(A) $\sqrt{\dfrac{2}{m}\left(\dfrac{1}{5}\dfrac{q^{2}}{4\pi \epsilon_{0} a}\right)^{1/2}}$
(B) $\sqrt{\dfrac{2}{m}\left(\dfrac{1}{15}\dfrac{q^{2}}{4\pi \epsilon_{0} a}\right)^{1/2}}$
(C) $\sqrt{\dfrac{2}{m}\left(\dfrac{4}{15}\dfrac{q^{2}}{4\pi \epsilon_{0} a}\right)^{1/2}}$
(D) $\sqrt{\dfrac{2}{m}\left(\dfrac{2}{15}\dfrac{q^{2}}{4\pi \epsilon_{0} a}\right)^{1/2}}$

Q60·PhysicsSingle correctJEE Main 2019

A system of three charges are placed as shown in the figure: If D >> d, the potential energy of the system is best given by:

(A) $\frac{1}{4\pi\varepsilon_o}\left[-\frac{q^2}{d}-\frac{qQd}{D^2}\right]$
(B) $\frac{1}{4\pi\varepsilon_o}\left[-\frac{q^2}{d}-\frac{qQd}{2D^2}\right]$
(C) $\frac{1}{4\pi\varepsilon_o}\left[-\frac{q^2}{d}+\frac{2qQd}{D^2}\right]$
(D) $\frac{1}{4\pi\varepsilon_o}\left[+\frac{q^2}{d}-\frac{qQd}{D^2}\right]$

Q61·PhysicsSingle correctJEE Main 2019

A solid conducting sphere, having a charge Q, is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge of −4 Q, the new potential difference between the same two surface is:

(A)2 V
(B)−2V
(C)4 V
(D)V

Q62·PhysicsSingle correctJEE Main 2019

The election field in a region is given by

\vec{E} = (Ax + B)\hat{i}

where E is in NC

^{-1}

and x in meters. The values of constants are A = 20 SI unit and B = 10 SI unit. If the potential at x =1 is V

_1

and that at x =

-

5 is V

_2

then V

_1

- V

_2

is:

(A)320 V
(B) $-$ 48 V
(C) $-$ 520 V
(D)180 V

Q63·PhysicsSingle correctJEE Main 2019

A positive point charge is released from rest at a distance

r_0

from a positive line charge with uniform density. The speed (v) of the point charge, as a function of instantaneous distance r from line charge, is proportional to

(A) $v \propto e^{+r/r_0}$
(B) $v \propto \ln\left(\dfrac{r}{r_0}\right)$
(C) $v \propto \sqrt{\ln\left(\dfrac{r}{r_0}\right)}$
(D) $v \propto \left(\dfrac{r}{r_0}\right)$

Q64·PhysicsSingle correctJEE Main 2019

There is a uniform spherically symmetric surface charge density at a distance

R_0

from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed V(R(t)) of the distribution as a function of its instantaneous radius R(t) is:

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

Q65·PhysicsSingle correctJEE Main 2019

An electric field of 1000V/m is applied to an electric dipole at angle of 45°. The value of electric dipole moment is 10

^{-29}

C.m. What is the potential energy of the electric dipole?

(A) $-20\times10^{18}$ J
(B) $-7\times10^{-27}$ J
(C) $-10\times10^{-29}$ J
(D) $-9\times10^{-20}$ J

Q66·PhysicsSingle correctJEE Main 2019

The give graph shown variation (with distance r from centre) of:

(A)Electric field of a uniformly charged sphere
(B)Potential of a uniformly charged spherical shell
(C)Potential of a uniformly charged sphere
(D)Electric field of a uniformly charged spherical shell

Q67·PhysicsSingle correctJEE Main 2019

A particle of mass m and charge q is in an electric and magnetic field given by:

\vec{E}=2\hat{i}+3\hat{j}; B=4\hat{j}+6\hat{k}

The charged particle is shifted from the origin to the point P(x = 1; y = 1) along a straight path. The magnitude of the total work done is:

(A)(0.35)q
(B)5q
(C)(2.5)q
(D)(0.15)q

Q68·PhysicsSingle correctJEE Main 2019

Three charges Q, +q and +q are placed at the vertices of a right – angle isosceles triangle as shown below. The net electrostatic energy of the configuration is zero, if the value of Q is:

(A)+q
(B) $\frac{-\sqrt{2}q}{\sqrt{2}+1}$
(C) $\frac{-q}{1+\sqrt{2}}$
(D)–2q

Q69·PhysicsSingle correctJEE Main 2019

Two electric dipoles A, B with respective dipole moments

\vec{d_{A}}=-4qa\hat{i}

and

\vec{d_{B}}=2qa\hat{i}

are placed on the x-axis with a separation R, as shown in the figure. The distance from A at which both of them produce the same potential is:

(A) $\frac{R}{\sqrt{2}+1}$
(B) $\frac{\sqrt{2}R}{\sqrt{2}+1}$
(C) $\frac{R}{\sqrt{2}-1}$
(D) $\frac{\sqrt{2}R}{\sqrt{2}-1}$

Q70·PhysicsSingle correctJEE Main 2019

A charge Q is distributed over three concentric spherical shell of radii a, b, c (a < b < c) such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common centre, where r < a, would be:

(A) $\dfrac{Q}{12\pi\epsilon_{0}}\dfrac{ab+bc+ca}{abc}$
(B) $\dfrac{Q\left(a^{2}+b^{2}+c^{2}\right)}{4\pi\epsilon_{0}\left(a^{3}+b^{3}+c^{3}\right)}$
(C) $\dfrac{Q}{4\pi\epsilon_{0}\left(a+b+c\right)}$
(D) $\dfrac{Q\left(a+b+C\right)}{4\pi\epsilon_{0}\left(a^{2}+b^{2}+c^{2}\right)}$

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