Electric Potential and Potential Difference

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JEE Main 2019

LEVELJEE Main

The given graph shows variation (with distance $r$ from centre) of

(A)

electric field of a uniformly charged spherical shell

(B)

potential of a uniformly charged spherical shell

(C)

electric field of a uniformly charged sphere

(D)

potential of a uniformly charged sphere

JEE Main 2019

LEVELJEE Advanced

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

(A)

\frac{Q ( a ^{2} + b ^{2} + c ^{2} )}{4 π ε _{0} ( a ^{3} + b ^{3} + c ^{3} )}

(B)

\frac{Q ( a + b + c )}{4 π ε _{0} ( a ^{2} + b ^{2} + c ^{2} )}

(C)

\frac{Q}{4 π ε _{0} ( a + b + c )}

(D)

\frac{Q ( ab + b c + c a )}{12 π ε _{0} ab c}

JEE Advanced 1999

LEVELJEE Advanced

A non-conducting disc of radius $a$ and uniform positive surface charge density $σ$ is placed on the ground with its axis vertical. A particle of mass $m$ and positive charge $q$ is dropped, along the axis of the disc from a height $H$ with zero initial velocity. The particle has $q / m = 4 ε_{0} g / σ$ . (a) Find the value of $H$ if the particle just reaches the disc. (b) Sketch the potential energy of the particle as a function of its height and find its equilibrium position.

LEVELJEE Main

Assertion For practical purposes, the earth is used as a reference at zero potential in electrical circuits. Reason The electrical potential of a sphere of radius $R$ with charge $Q$ uniformly distributed on the surface is given by $\frac{Q}{4 π ε _{0} R}$ .

(A)

If Assertion is true, Reason is true; Reason is the correct explanation for Assertion.

(B)

If Assertion is true, Reason is true; Reason is not a correct explanation for Assertion.

(C)

If Assertion is true; Reason is false.

(D)

If Assertion is false; Reason is true.

LEVELJEE Main

A uniform electric field pointing in positive x-direction exists in a region. Let $A$ be the origin, $B$ be the point on the x-axis at $x = + 1 cm$ and $C$ be the point on the y-axis at $y = + 1 cm$ . Then the potentials at the points $A$ , $B$ and $C$ satisfy

(A)

V_{A} < V_{B}

(B)

V_{A} > V_{B}

(C)

V_{A} < V_{C}

(D)

V_{A} > V_{C}

JEE Advanced 2000

LEVELJEE Advanced

Four point charges $+ 8 μ C, - 1 μ C, - 1 μ C$ and $+ 8 μ C$ are fixed at the points $- 27/2 m, - 3/2 m, + 3/2 m$ and $+ 27/2 m$ respectively on the $y$ -axis. A particle of mass $6 \times 1 0^{- 4} kg$ and charge $+ 0.1 μ C$ moves along the $x$ -direction. Its speed at $x = + \infty$ is $v_{0}$ . Find the least value of $v_{0}$ for which the particle will cross the origin. Find also the kinetic energy of the particle at the origin. Assume that space is gravity free. $(1/4 π ε_{0} = 9 \times 1 0^{9} Nm^{2} / C^{2})$

LEVELBoard

A hollow metal sphere of radius $5 cm$ is charged such that the potential on its surface is $10 V$ . The potential at the centre of the sphere is

(A)

zero

(B)

10 V

(C)

same as at a point

5 cm

away from the surface

(D)

same as at a point

25 cm

away from the surface

JEE Advanced 2005

LEVELJEE Advanced

A conducting bubble of radius $a$ , thickness $t$ ( $t << a$ ) has potential $V$ . Now the bubble collapses into a droplet. Find the potential of the droplet.

LEVELJEE Main

A non-conducting ring of radius $0.5 m$ carries a total charge of $1.11 \times 1 0^{- 10} C$ distributed non-uniformly on its circumference producing an electric field $E$ everywhere in space. The value of the integral $\int_{l = \infty}^{l = 0} - E \cdot d l$ ( $l = 0$ being centre of the ring) in volt is

(A)

+ 2

(B)

- 1

(C)

- 2

(D)

zero

JEE Advanced 2006

LEVELJEE Main

For spherical symmetrical charge distribution, variation of electric potential with distance from centre is given in diagram. Given that $V = \frac{q}{4 π ε _{0} R _{0}}$ for $r \leq R_{0}$ and $V = \frac{q}{4 π ε _{0} r}$ for $r \geq R_{0}$ Then, which option(s) are correct

* Multiple Correct Options

(A)

Total charge within

2 R_{0}

q

(B)

Total electrostatic energy for

r \leq R_{0}

is zero

(C)

r = R_{0}

electric field is discontinuous

(D)

There will be no charge anywhere except at

r = R_{0}

LEVELJEE Main

A solid conducting sphere having a charge $Q$ is surrounded by an uncharged concentric 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 change of $- 3 Q$ , the new potential difference between the same two surfaces is

(A)

V

(B)

2 V

(C)

4 V

(D)

- 2 V

LEVELJEE Main

The electric potential $V$ at any point $x, y, z$ (all in metre) in space is given by $V = 4 x^{2}$ volt. The electric field at the point $(1 m, 0, 2 m)$ is ……… V/m.

JEE Advanced 1981

LEVELJEE Main

A charge $Q$ is distributed over two concentric hollow spheres of radii $r$ and $R$ ( $> r$ ) such that the surface densities are equal. Find the potential at the common centre.

JEE Advanced 1990

LEVELJEE Advanced

Three concentric spherical metallic shells, $A$ , $B$ and $C$ of radii $a$ , $b$ and $c$ ( $a < b < c$ ) have surface charge densities $σ$ , $- σ$ and $σ$ respectively. (a) Find the potential of the three shells $A$ , $B$ and $C$ . (b) If the shells $A$ and $C$ are at the same potential, obtain the relation between the radii $a$ , $b$ and $c$ .

JEE Advanced 2007

LEVELJEE Main

Positive and negative point charges of equal magnitude are kept at $(0, 0, a /2)$ and $(0, 0, - a /2)$ , respectively. The work done by the electric field when another positive point charge in moved from $(- a, 0, 0)$ to $(0, a, 0)$ is

depends on the path connecting the initial and final positions

JEE Advanced 1991

LEVELJEE Advanced

Two fixed charges $- 2 Q$ and $Q$ are located at the points with coordinates $(- 3 a, 0)$ and $(+ 3 a, 0)$ respectively in the $x - y$ plane. (1991) (a) Show that all points in the $x - y$ plane where the electric potential due to the two charges is zero, lie on a circle. Find its radius and the location of its centre. (b) Give the expression $V (x)$ at a general point on the $x$ -axis and sketch the function $V (x)$ on the whole $x$ -axis. (c) If a particle of charge $+ q$ starts form rest at the centre of the circle, show by a short quantitative argument that the particle eventually crosses the circle. Find its speed when it does so.

LEVELJEE Advanced

Three concentric spherical metallic shells, $A$ , $B$ and $C$ of radii $a$ , $b$ and $c$ ( $a < b < c$ ) have surface charge densities $σ$ , $- σ$ and $σ$ respectively. (a) Find the potential of the three shells $A$ , $B$ and $C$ . (b) If the shells $A$ and $C$ are at the same potential, obtain the relation between the radii $a$ , $b$ and $c$ .

LEVELJEE Main

A point charge $q$ moves from point $P$ to point $S$ along the path $P QR S$ (Fig.) in a uniform electric field $E$ pointing parallel to the positive direction of the $X$ -axis. The coordinates of points $P, Q, R$ and $S$ are $(a, b, 0), (2 a, 0, 0), (a, - b, 0), (0, 0, 0)$ respectively. The work done by the field in the above process is given by the expression ...... .

LEVELJEE Main

There are two large parallel metallic plates $S_{1}$ and $S_{2}$ carrying surface charge densities $σ_{1}$ and $σ_{2}$ respectively ( $σ_{1} > σ_{2}$ ) placed at a distance $d$ apart in vacuum. Find the work done by the electric field in moving a point charge $q$ a distance $a (a < d)$ from $S_{1}$ towards $S_{2}$ along a line making an angle $π /4$ with the normal to the plates.

LEVELJEE Main

Two identical thin rings, each of radius $R$ , are coaxially placed a distance $R$ apart. If $Q_{1}$ and $Q_{2}$ are respectively the charges uniformly spread on the two rings, the work done in moving a charge $q$ from the centre of one ring to that of the other is

(A)

zero

(B)

\frac{q ( Q _{1} - Q _{2} ) ( 2 - 1 )}{2 ( 4 π ε _{0} R )}

(C)

\frac{q 2 ( Q _{1} + Q _{2} )}{( 4 π ε _{0} R )}

(D)

\frac{q ( Q _{1} + Q _{2} ) ( 2 + 1 ) 2}{( 4 π ε _{0} R )}

LEVELJEE Main

Figure shows lines of constant potential in a region in which an electric field is present. The values of the potential are written in brackets. Of the points $A$ , $B$ and $C$ , the magnitude of the electric field is greatest at the point…… .

JEE Advanced 1993

LEVELJEE Advanced

A circular ring of radius $R$ with uniform positive charge density $λ$ per unit length is located in the $y$ - $z$ plane with its centre at the origin $O$ . A particle of mass $m$ and positive charge $q$ is projected from the point $P (R 3, 0, 0)$ on the positive $x$ -axis directly towards $O$ , with an initial speed $v$ . Find the smallest (non-zero) value of the speed $v$ such that the particle does not return to $P$ .

JEE Advanced 2021

LEVELJEE Advanced

Comprehension Passage

Two point charges

- Q

and

+ Q / 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.

Question 1:

The value of R is _____ meter.

Question 2:

The value of b is _____ meter.

JEE Advanced 2024

LEVELJEE Advanced

An infinitely long thin wire, having a uniform charge density per unit length of $5 nC/m$ , is passing through a spherical shell of radius $1 m$ , as shown in the figure. A $10 nC$ 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 $\frac{1}{4 π ε _{0}} = 9 \times 1 0^{9}$ , $ln 2 = 0.7$ . Ignore the area pierced by the wire.]

JEE Advanced 2019

LEVELJEE Advanced

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 $α 4 π R^{2}$ ( $α ≪ 1$ ) is made on the shell without affecting the rest of the shell. Which one of the following statements is correct ?

(A)

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 - α}{1 - 2 α}

(B)

The magnitude of electric field at the center of the shell is reduced by

\frac{α V _{0}}{2 R}

(C)

The magnitude of electric field at a point, located on a line passing through the hole and shell's center on a distance

2 R

from the center of the spherical shell will be reduced by

\frac{α V _{0}}{2 R}

(D)

The potential at the center of the shell is reduced by

2 α V_{0}

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The given graph shows variation (with distance r from centre) of

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A hollow metal sphere of radius 5 cm is charged such that the potential on its surface is 10 V. The potential at the centre of the sphere is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A conducting bubble of radius a, thickness t (t<<a) has potential V. Now the bubble collapses into a droplet. Find the potential of the droplet.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The electric potential V at any point x,y,z (all in metre) in space is given by V=4x2 volt. The electric field at the point (1 m,0,2 m) is ……… V/m.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A charge Q is distributed over two concentric hollow spheres of radii r and R (>r) such that the surface densities are equal. Find the potential at the common centre.

Comprehension Passage

The value of R is _____ meter.

The value of b is _____ meter.

The given graph shows variation (with distance $r$ from centre) of

A hollow metal sphere of radius $5 cm$ is charged such that the potential on its surface is $10 V$ . The potential at the centre of the sphere is

A conducting bubble of radius $a$ , thickness $t$ ( $t << a$ ) has potential $V$ . Now the bubble collapses into a droplet. Find the potential of the droplet.

The electric potential $V$ at any point $x, y, z$ (all in metre) in space is given by $V = 4 x^{2}$ volt. The electric field at the point $(1 m, 0, 2 m)$ is ……… V/m.

A charge $Q$ is distributed over two concentric hollow spheres of radii $r$ and $R$ ( $> r$ ) such that the surface densities are equal. Find the potential at the common centre.