# JEE Advanced > Electrostatics

Explore popular questions from Electrostatics for JEE Advanced. This collection covers Electrostatics previous year JEE Advanced questions hand picked by experienced teachers.

Physics
Chemistry
Mathematics
Q 1.

Correct4

Incorrect-1

Two point charges {tex} + q {/tex} and {tex} - q {/tex} are held fixed at {tex} ( - d , o ) {/tex} and {tex} ( d , o ) {/tex} respectively of a {tex} x - y {/tex} coordinate system. Then

A

The electric field {tex} E {/tex} at all points on the {tex} x {/tex} -axis has the same direction

Electric field at all points on {tex} y {/tex} -axis is along {tex} x {/tex} -axis

C

Work has to be done in bringing a test charge from {tex}\infty {/tex} to the origin

D

The dipole moment is {tex} 2 q d {/tex} along the {tex} x {/tex} -axis

##### Explanation

Q 2.

Correct4

Incorrect-1

A parallel plate capacitor of capacitance {tex} C {/tex} is connected to a battery and is charged to a potential difference {tex} V {/tex}. Another capacitor of capacitance {tex} 2 C {/tex} is similarly charged to a potential difference {tex} 2 V {/tex}. The charging battery is now disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is

A

zero

{tex} \frac { 3 } { 2 } C V ^ { 2 } {/tex}

C

{tex} \frac { 25 } { 6 } C V ^ { 2 } {/tex}

D

{tex} \frac { 9 } { 2 } C V ^ { 2 } {/tex}

##### Explanation

Q 3.

Correct4

Incorrect-1

Two identical metal plates are given positive charges {tex} Q _ { 1 } {/tex} and {tex} Q _ { 2 } \left( < Q _ { 1 } \right) {/tex} respectively. If they are now brought close together to form a parallel plate capacitor with capacitance {tex} C , {/tex} the potential difference between them is

A

{tex} \left( Q _ { 1 } + Q _ { 2 } \right) / ( 2 C ) {/tex}

B

{tex} \left( Q _ { 1 } + Q _ { 2 } \right) / C {/tex}

C

{tex} \left( Q _ { 1 } - Q _ { 2 } \right) / C {/tex}

{tex} \left( Q _ { 1 } - { Q } _ { 2 } \right) / ( 2 C ) {/tex}

##### Explanation

Q 4.

Correct4

Incorrect-1

Three charges {tex} Q , + q {/tex} and {tex} + q {/tex} are placed at the vertices of a right-angled isosceles triangle as shown. The net electrostatic energy of the configuration is zero if {tex} Q {/tex} is equal to

A

{tex} \frac { - q } { 1 + \sqrt { 2 } } {/tex}

{tex} \frac { - 2 q } { 2 + \sqrt { 2 } } {/tex}

C

{tex} - 2 q {/tex}

D

{tex} + q {/tex}

##### Explanation

Q 5.

Correct4

Incorrect-1

A parallel plate capacitor of area {tex} A , {/tex} plate separation {tex} d {/tex} and capacitance {tex} C {/tex} is filled with three different dielectric materials having dielectric constants {tex} k _ { 1 } , k _ { 2 } {/tex} and {tex} k _ { 3 } {/tex} as shown. If a single dielectric material is to be used to have the same capacitance {tex} C {/tex} in this capacitor, then its dielectric constant {tex} k {/tex} is given by

A

{tex} \frac { 1 } { K } = \frac { 1 } { K _ { 1 } } + \frac { 1 } { K _ { 2 } } + \frac { 1 } { 2 K _ { 3 } } {/tex}

{tex} \frac { 1 } { K } = \frac { 1 } { K _ { 1 } + K _ { 2 } } + \frac { 1 } { 2 K _ { 3 } } {/tex}

C

{tex} K = \frac { K _ { 1 } K _ { 2 } } { K _ { 1 } + K _ { 2 } } + 2 K _ { 3 } {/tex}

D

{tex} K = K _ { 1 } + K _ { 2 } + 2 K _ { 3 } {/tex}

##### Explanation

Q 6.

Correct4

Incorrect-1

Three positive charges of equal value {tex} q {/tex} are placed at the vertices of an equilateral triangle. The resulting lines of force should be sketched as in

A

B

D

##### Explanation

Q 7.

Correct4

Incorrect-1

Consider the situation shown in the figure. The capacitor {tex} A {/tex} has a charge {tex} q {/tex} on it whereas {tex} B {/tex} is uncharged. The charge appearing on the capacitor {tex} B {/tex} a long time after the switch is closed is

zero

B

{tex} q / 2 {/tex}

C

{tex} q {/tex}

D

{tex} 2 q {/tex}

##### Explanation

Q 8.

Correct4

Incorrect-1

Two identical capacitors, have the same capacitance {tex} C . {/tex} One of them is charged to potential {tex} V _ { 1 } {/tex} and the other {tex} V _ { 2 } . {/tex} The negative ends of the capacitors are connected together. When the positive ends are also connected, the decrease in energy of the combined system is

A

{tex} \frac { 1 } { 4 } C \left( V _ { 1 } ^ { 2 } - V _ { 2 } ^ { 2 } \right) {/tex}

B

{tex} \frac { 1 } { 4 } C \left( V _ { 1 } ^ { 2 } + V _ { 2 } ^ { 2 } \right) {/tex}

{tex} \frac { 1 } { 4 } C \left( V _ { 1 } - V _ { 2 } \right) ^ { 2 } {/tex}

D

{tex} \frac { 1 } { 4 } C \left( V _ { 1 } + V _ { 2 } \right) ^ { 2 } {/tex}

##### Explanation

Q 9.

Correct4

Incorrect-1

A metallic shell has a point charge {tex} ^ { \prime } q ^ { \prime } {/tex} kept inside its cavity. Which one of the following diagrams correctly represents the electric lines of forces?

A

B

D

##### Explanation

Q 10.

Correct4

Incorrect-1

Six charges of equal magnitude, 3 positive and 3 negative are to be placed on {tex} P Q R S T U {/tex} corners of a regular hexagon, such that field at the centre is double that of what it would have been if only one +ve charge is placed at {tex} R . {/tex} Which of the following arrangement of charge is possible for {tex} P , Q , R , S, T{/tex} and {tex}U{/tex} respectively.

A

{tex} + , + , + , - , - , - {/tex}

B

{tex} - , + , + , + , - , - {/tex}

{tex} - , + , + , - , + , - {/tex}

D

{tex} + , - , + , - , + , - {/tex}

##### Explanation

Q 11.

Correct4

Incorrect-1

A Gaussian surface in the figure is shown by dotted line. The electric field on the surface will be

A

due to {tex} q _ { 1 } {/tex} and {tex} q _ { 2 } {/tex} only

B

due to {tex} q _ { 2 } {/tex} only

C

Zero

due to all

##### Explanation

Q 12.

Correct4

Incorrect-1

Three infinitely long charge sheets are placed as shown in figure. The electric field at point {tex} P {/tex} is

A

{tex} \frac { 2 \sigma } { \varepsilon _ { 0 } } \hat { k } {/tex}

B

{tex} \frac { 4 \sigma } { \varepsilon _ { 0 } } \hat { k } {/tex}

{tex} - \frac { 2 \sigma } { \varepsilon _ { 0 } } \hat { k } {/tex}

D

{tex} - \frac { 4 \sigma } { \varepsilon _ { 0 } } \hat { k } {/tex}

##### Explanation

Q 13.

Correct4

Incorrect-1

A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is

A

zero everywhere

non-zero and uniform

C

non-uniform

D

zero only at its center

##### Explanation

Q 14.

Correct4

Incorrect-1

Consider a system of three charges {tex} q / 3 , q / 3 {/tex} and {tex} - 2 q / 3 {/tex} placed at points {tex} A , B {/tex} and {tex} C , {/tex} respectively, as shown in the figure. Take {tex} O {/tex} to be the centre of the circle of radius {tex} \mathrm { R } {/tex} and angle {tex} C A B = 60 ^ { \circ } {/tex}

A

The electric field at point {tex} O {/tex} is {tex} \frac { q } { 8 \pi \varepsilon _ { 0 } R ^ { 2 } } {/tex} directed along the negative {tex} x {/tex} -axis

B

The potential energy of the system is zero

The magnitude of the force between the charges at {tex} C {/tex} and {tex} B {/tex} is {tex} \frac { q ^ { 2 } } { 54 \pi \varepsilon _ { 0 } R ^ { 2 } } {/tex}

D

The potential at point {tex} O {/tex} is {tex} \frac { q } { 12 \pi \varepsilon _ { 0 } R } {/tex}

##### Explanation

Q 15.

Correct4

Incorrect-1

Three concentric metallic spherical shells of radii {tex} R , 2 R , 3 R , {/tex} are given charges {tex} Q _ { 1 } , Q _ { 2 } , Q _ { 3 } , {/tex} respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells, {tex} Q _ { 1 }: Q _ { 2 }: Q _ { 3 } , {/tex} is

A

1: 2: 3

1: 3: 5

C

1: 4: 9

D

1: 8: 18

##### Explanation

Q 16.

Correct4

Incorrect-1

A disc of radius {tex} a / 4 {/tex} having a uniformly distributed charge {tex} 6 \mathrm { C } {/tex} is placed in the {tex} x - y {/tex} plane with its centre at {tex} ( - a / 2,0,0 ) {/tex}. A rod of length {tex} a {/tex} carrying a uniformly distributed charge {tex} 8 \mathrm { C } {/tex} is placed on the {tex} x - {/tex} axis from {tex} x = a / 4 {/tex} to {tex} x = 5 a / 4 {/tex}. Two point
charges {tex} - 7 \mathrm { C } {/tex} and {tex} 3 \mathrm { C } {/tex} are placed at {tex} ( a / 4 , - a / 4,0 ) {/tex} and {tex} ( - 3 a / 4,3 a / 4,0 ) , {/tex} respectively. Consider a cubical surface formed by six surfaces {tex} x = \pm a / 2 , y = \pm a / 2 , z = \pm a / 2 . {/tex} The electric flux through this cubical surface is

{tex} \frac { - 2 C } { \varepsilon _ { 0 } } {/tex}

B

{tex} \frac { 2 C } { \varepsilon _ { 0 } } {/tex}

C

{tex} \frac { 10 C } { \varepsilon _ { 0 } } {/tex}

D

{tex} \frac { 12 C } { \varepsilon _ { 0 } } {/tex}

##### Explanation

Q 17.

Correct4

Incorrect-1

Consider an electric field {tex} \vec { E } = E _ { 0 } \hat { x } {/tex} where {tex} \mathrm { E } _ { 0 } {/tex} is a constant. The flux through the shaded area (as shown in the figure) due to this field is

A

{tex} 2 E _ { 0 } a _ { 2 } {/tex}

B

{tex} \sqrt { 2 } E _ { 0 } a ^ { 2 } {/tex}

{tex} E _ { 0 } \mathrm { a } ^ { 2 } {/tex}

D

{tex} \frac { E _ { 0 } a ^ { 2 } } { \sqrt { 2 } } {/tex}

##### Explanation

Q 18.

Correct4

Incorrect-1

In the given arrangement of capacitors, {tex} 6 \mu \mathrm { C } {/tex} charge is added to point {tex} a {/tex}. Find the charge on upper capacitor

{tex} 3 \mu \mathrm { C } {/tex}

B

{tex} 1 \mu \mathrm { C } {/tex}

C

{tex} 2 \mu \mathrm {C} {/tex}

D

{tex} 6 \mu \mathrm { C } {/tex}

##### Explanation

Q 19.

Correct4

Incorrect-1

Consider three concentric shells of metal {tex} A , B {/tex} and {tex} C {/tex} are having radii {tex} a , b {/tex} and {tex} c {/tex} respectively as shown in the figure {tex} ( a < b < c ) {/tex}. Their surface charge densities are {tex} \sigma , - \sigma {/tex} and {tex} \sigma {/tex} respectively. Calculate the electric potential on the surface of shell {tex} A {/tex}

{tex} \frac { \sigma } { \varepsilon _ { 0 } } ( a - b + c ) {/tex}

B

{tex} \frac { \sigma } { \varepsilon _ { 0 } } ( a - b - c ) {/tex}

C

{tex} \frac { \sigma } { \varepsilon _ { 0 } } \left( a ^ { 2 } + b ^ { 2 } + c ^ { 2 } \right) {/tex}

D

{tex} \frac { \sigma } { \varepsilon _ { 0 } } ( a + b - c ) {/tex}

##### Explanation

Q 20.

Correct4

Incorrect-1

Three capacitors of capacitance {tex} 1 \mu \mathrm { F } , 2 \mu \mathrm { F } {/tex} and {tex} 3 \mu \mathrm { F } {/tex} are connected in series and a potential difference of {tex} 11 \mathrm { V } {/tex} is applied across the combination. Then, the potential difference across the plate of {tex} 1 \mu \mathrm { F } {/tex} capacitor is

A

{tex} 2 \mathrm { V } {/tex}

B

{tex} 4 \mathrm { V } {/tex}

C

{tex} 1 \mathrm { V } {/tex}

{tex} 6 \mathrm { V } {/tex}

##### Explanation

Q 21.

Correct4

Incorrect-1

An electric charge {tex} 10 ^ { - 3 }\mu \mathrm { C } {/tex} is placed at the origin {tex} ( 0,0 ) {/tex} of {tex} X -Y{/tex} coordinate system. Two points {tex} A {/tex} and {tex} B {/tex} are situated at {tex} ( \sqrt { 2 } , \sqrt { 2 } ) {/tex} and {tex} ( 2,0 ) {/tex} respectively. The potential difference between the points {tex} A {/tex} and {tex} B {/tex} will be

A

{tex} 9 \mathrm { V } {/tex}

Zero

C

{tex} 2 \mathrm { V } {/tex}

D

{tex} 4.5 \mathrm { V } {/tex}

##### Explanation

Q 22.

Correct4

Incorrect-1

The potential to which a conductor is raised, depends on

A

The amount of charge

B

Geometry and size of the conductor

Both (a) and (b)

D

Only on (a)

Q 23.

Correct4

Incorrect-1

Three capacitors {tex} C _ { 1 } , C _ { 2 } {/tex} and {tex} C _ { 3 } {/tex} are connected as shown in the figure to a battery of {tex} V {/tex} volt. If the capacitor {tex} C _ { 3 } {/tex} breaks down electrically the change in total charge on the combination of capacitors is

{tex} \left( C _ { 1 } + C _ { 2 } \right) V \left[ 1 - \left( \frac { C _ { 3 } } { C _ { 1 } + C _ { 2 } + C _ { 3 } } \right) \right] {/tex}

B

{tex} \left( C _ { 1 } + C _ { 2 } \right) V \left[ 1 - \left( \frac { \left( C _ { 1 } + C _ { 2 } \right) } { C _ { 1 } + C _ { 2 } + C _ { 3 } } \right) \right] {/tex}

C

{tex} \left( C _ { 1 } + C _ { 2 } \right) V \left[ 1 + \left( \frac { C _ { 3 } } { C _ { 1 } + C _ { 2 } + C _ { 3 } } \right) \right] {/tex}

D

{tex} \left( C _ { 1 } + C _ { 2 } \right) V \left[ 1 + \left( \frac { C _ { 2 } } { C _ { 1 } + C _ { 2 } + C _ { 3 } } \right) \right] {/tex}

##### Explanation

Q 24.

Correct4

Incorrect-1

Two charges {tex} + q {/tex} and {tex} - q {/tex} are kept apart. Then at any point on the right bisector of line joining the two charges

A

The electric field strength is zero

The electric potential is zero

C

Both electric potential and electric field strength are zero.

D

Both electric potential and electric field strength are non-zero.

##### Explanation

Q 25.

Correct4

Incorrect-1

An electric field is expressed as {tex} \vec { E } = 2 \hat { \imath } + 3 \hat { j } {/tex}. Find the potential difference {tex} \left( V _ { A } - V _ { B } \right) {/tex} between two points {tex} A {/tex} and {tex} B {/tex} whose position vectors are given by {tex} r _ { A } = \hat { \imath } + 2 \hat { j } {/tex} and {tex} r _ { B } = 2 \hat { \imath } + \hat { \jmath } + 3 \hat { k } {/tex}

{tex} - 1 \mathrm { V } {/tex}

B

{tex} 1 \mathrm { V } {/tex}

C

{tex} 2 \mathrm { V } {/tex}

D

{tex} 3 \mathrm { V } {/tex}