# JEE Main

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

## Mathematics

Electrostatics

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Q 1. Using mass {tex}\mathrm{(M)}{/tex}, length {tex}\mathrm{(L)}{/tex}, time {tex}\mathrm{(T)}{/tex} and current {tex}\mathrm{(A)}{/tex} as fundamental quantities, the dimension of permittivity is:

A

{tex} \mathrm { ML } ^ { - 2 } \mathrm { T } ^ { 2 } \mathrm { A } {/tex}

{tex} \mathrm { M } ^ { - 1 } \mathrm { L } ^ { - 3 } \mathrm { T } ^ { 4 } \mathrm { A } ^ { 2 } {/tex}

C

{tex} \mathrm { MLT } ^ { - 2 } \mathrm { A } {/tex}

D

{tex} \mathrm { ML } ^ { 2 } \mathrm { T } ^ { - 1 } \mathrm { A } ^ { 2 } {/tex}

##### Explanation

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Q 2. Two point charges {tex} + 9 \ \mathrm e {/tex} and {tex} + \mathrm e {/tex} are kept {tex} 16 \mathrm { cm } {/tex}. apart from each other. Where should a third charge {tex} \mathrm { q } {/tex} be placed between them so that the system is in equilibrium state:

A

{tex} 24 \mathrm { cm } {/tex} from {tex} + 9 \mathrm { e } {/tex}

{tex} 12 \mathrm { cm } {/tex} from {tex} + 9 \mathrm { e } {/tex}

C

{tex} 24 \mathrm { cm } {/tex} from {tex} + \mathrm e {/tex}

D

{tex} 12 \mathrm { cm } {/tex} from {tex} + \mathrm { e } {/tex}

##### Explanation

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Q 3. Four charges are arranged at the comers of a square {tex} \mathrm { ABCD } {/tex} as shown in the figure. The force on the charge kept at the centre {tex}\mathrm O{/tex} will be:

A

perpendicular to side {tex}\mathrm {AB}{/tex}

along the diagonal {tex}\mathrm {BD}{/tex}

C

along the diagonal {tex}\mathrm {AC}{/tex}

D

Zero

##### Explanation

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Q 4. Two infinite linear charges are placed parallel other at a {tex} 0.1 \mathrm { m } {/tex} from each other. If the linear charge density on each is {tex} 5 \mu \mathrm { C } / \mathrm { m } , {/tex} the force acting on a unit length of each linear charge will be:

A

{tex} 2.5 \mathrm { N } / \mathrm { m } {/tex}

B

{tex} 3.25 \mathrm { N } / \mathrm { m } {/tex}

{tex} 4.5 \mathrm { N } / \mathrm { m } {/tex}

D

{tex} 7.5 \mathrm { N } / \mathrm { m } {/tex}

##### Explanation

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Q 5. An electron of mass {tex} m _ { e } , {/tex} initially at rest, moves through a certance in a uniform electric field in tin {tex} t _ { 1 } {/tex}. A proton of mass {tex} m _ { p } , {/tex} also, initially at rest, takes time {tex} t _ { 2 } {/tex} to move through an equal distance in this unifor electric field. Neglecting the effect of gravity, the ratio {tex} t _ { 2 } / t _ { 1 } {/tex} is nearly equal to

A

{tex}1{/tex}

{tex} \left( \mathrm { m } _ { \mathrm { p } } / \mathrm { m } _ { \mathrm { e } } \right) ^ { 1 / 2 } {/tex}

C

{tex} \left( \mathrm { m } _ { \mathrm { e } } / \mathrm { m } _ { \mathrm { p } } \right) ^ { 1 / 2 } {/tex}

D

{tex}1836{/tex}

##### Explanation

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Q 6. An electron is projected as in figure with kinetic energy {tex} \mathrm { K } , {/tex} at an angle {tex} \theta = 45 {/tex} between two charged plates. The magnitude of the electric field so that the electron just fails to strike the upper plate, should be greater than:

A

{tex} \frac { \mathrm { K } } { \mathrm { qd } } {/tex}

B

{tex} \frac { 2 \mathrm { K } } { \mathrm { qd } } {/tex}

{tex} \frac { \mathrm { K } } { 2 \mathrm { qd } } {/tex}

D

Infinite

##### Explanation

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Q 7. A point charge {tex} 50 \mu C {/tex} is located in the {tex}\mathrm{XY}{/tex} plane at the point of position vector {tex} \vec { r } _ { 0 } = ( 2 \hat { i } + 3 \vec { j } ) {/tex} meter. What is the electric field at the point of position vector {tex} \vec { r } = ( 8 \vec { i } - 5 \vec { j } ) {/tex} meter:

A

{tex} 1200 \mathrm { V } / \mathrm { m } {/tex}

B

{tex} 0.04 \mathrm { V } / \mathrm { m } {/tex}

C

{tex} 900 \mathrm { V } / \mathrm { m } {/tex}

{tex} 4500 \mathrm { V } / \mathrm { m } {/tex}

##### Explanation

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Q 8. Three point charges {tex} 1 \mathrm { C } , 2 \mathrm { C } {/tex} and {tex} 3 \mathrm { C } {/tex} are placed at the corners of an equilateral triangle of side {tex} 1 \mathrm { m } {/tex}. The work required to move these charges to the corners of a smaller equilateral triangle of side {tex} 0.5 \mathrm { m } {/tex} in two different ways as in fig. {tex}\mathrm{(A)}{/tex} and fig. {tex}\mathrm{(B)}{/tex} are {tex} \mathrm { W } _ { \mathrm { a } } {/tex} and {tex} \mathrm { W } _ { \mathrm { b } } {/tex} then:

A

{tex} \mathrm { W } _ { \mathrm { a } } > \mathrm { W } _ { \mathrm { b } } {/tex}

B

{tex} \mathrm { W } _ { \mathrm { a } } < \mathrm { W } _ { \mathrm { b } } {/tex}

{tex} \mathrm { W } _ { \mathrm { a } } = \mathrm { W } _ { \mathrm { b } } {/tex}

D

{tex} \mathrm { W } _ { \mathrm { a } } = 0 {/tex} and {tex} \mathrm { W } _ { \mathrm { b } } = 0 {/tex}

##### Explanation

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Q 9. As per this diagram a point charge {tex} + q {/tex} is placed at the origin {tex} \mathrm O . {/tex} Work done in taking another point charge {tex}\mathrm { - Q} {/tex} from the point {tex}{tex}\mathrm { A( 0 , a ) }{/tex} to another point {tex}{tex}\mathrm {B ( a , 0 )} {/tex} along the straight path {tex} \mathrm { AB} {/tex} is :

A

{tex} \left( \frac { - q Q } { 4 \pi \epsilon _ { 0 } } \frac { 1 } { a ^ { 2 } } \right) \sqrt { 2 } {/tex} a

zero

C

{tex} \left( \frac { \mathrm { q } \mathrm { Q } } { 4 \pi \epsilon _ { 0 } } \frac { 1 } { \mathrm { a } ^ { 2 } } \right) \frac { 1 } { \sqrt { 2 } } {/tex}

D

{tex} \left( \frac { \mathrm { qQ } } { 4 \pi \epsilon _ { 0 } } \frac { 1 } { \mathrm { a } ^ { 2 } } \right) \sqrt { 2 } \mathrm { a } {/tex}

##### Explanation

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Q 10. In a regular polygon of {tex}n{/tex} sides, each comer is at a distance {tex} \mathrm { r } {/tex} from the center. Identical charges are placed at {tex} \mathrm { n-1 } {/tex} corners. At the centre, the intensity is {tex} \mathrm { E } {/tex} and the potential is {tex} \mathrm { V } {/tex}. The ratio {tex} \mathrm { V } / \mathrm { E } {/tex} has magnitude :

A

{tex} \mathrm { nr } {/tex}

{tex} \mathrm{( n - 1 ) r} {/tex}

C

{tex} \mathrm{( n - 1 ) / r }{/tex}

D

{tex} \mathrm{ r ( n - 1 ) / n }{/tex}

##### Explanation

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Q 11. An alpha particle of energy {tex}\mathrm{5 MeV}{/tex} is scattered through {tex}180 \degree{/tex} by a fixed uranium nucleus. The distance of closest approach is of the order:

A

{tex} 1{tex} {\text{Å}} {/tex}

B

{tex} 10 ^ { - 10 } \mathrm { cm } {/tex}

{tex} 10 ^ { - 12 } \mathrm { cm } {/tex}

D

{tex} 10 ^ { - 15 } \mathrm { cm } {/tex}

##### Explanation

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Q 12. A charge {tex}3{/tex} coulomb experiences a force {tex} 300 \mathrm { N } {/tex} when placed in a uniform electric field. The potential difference between two points separated by a distance of {tex} 10 \mathrm { cm } {/tex} along the field line is:

{tex} 10 \mathrm { V } {/tex}

B

{tex} 90 \mathrm { v } {/tex}

C

{tex} 1000 \mathrm { V } {/tex}

D

{tex} 9000 \mathrm { V } {/tex}

##### Explanation

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Q 13. Uniform electric field of magnitude {tex} 100 \mathrm { V } / \mathrm { m } {/tex} in space is directed along the line {tex} \mathrm { y } = 3 + \mathrm { x } . {/tex} Find the potential difference between point {tex} \mathrm { A } ( 3,1 ) {/tex} & {tex}\mathrm { B } ( 1,3 ): {/tex}

A

{tex} 100 \mathrm { V } {/tex}

B

{tex} 200 \sqrt { 2 } \mathrm { V } {/tex}

C

{tex} 200 \mathrm { V } {/tex}

{tex}0{/tex}

##### Explanation

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Q 14. The equation of an equipotential line in an electric field is {tex} y = 2 x , {/tex} then the electric field strength vector at {tex} ( 1,2 ) {/tex} may be

A

{tex} 4 \tilde { i } + 3 \tilde { j } {/tex}

B

{tex} 4 \tilde { i } + 8 \tilde { j } {/tex}

C

{tex} 8\tilde i + 4\tilde j {/tex}

{tex} - 8 \tilde i + 4 \tilde j {/tex}

##### Explanation

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Q 15. In a certain region of space, the potential is given by {tex} V = k \left( 2 x ^ { 2 } - y ^ { 2 } + z ^ { 2 } \right) . {/tex} The electric field at the point (1,1,1) magnitude :

A

{tex} \mathrm { k } \sqrt { 6 } {/tex}

{tex} 2 \mathrm { k } \sqrt { 6 } {/tex}

C

{tex} 2 \mathrm k \sqrt { 3 } {/tex}

D

{tex} 4 \mathrm k \sqrt { 3 } {/tex}

##### Explanation

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Q 16. The figure below shows two equipotential lines in {tex} \mathrm { XY } {/tex} plane for an electric field. The scales are marked. The {tex} \mathrm { X } {/tex}- component {tex} \mathrm { E } _ { \mathrm { x } } {/tex} and {tex} \mathrm { Y } {/tex} -component {tex} \mathrm { E } _ { \mathrm { y } } {/tex} of the electric field in the space between these equipotential lines are respectively :

A

{tex} + 100 \mathrm { V } / \mathrm { m } , - 200 \mathrm { V } / \mathrm { m } {/tex}

B

{tex} + 200 \mathrm { V } / \mathrm { m } , + 100 \mathrm { V } / \mathrm { m } {/tex}

{tex} - 100 \mathrm { V } / \mathrm { m } , + 200 \mathrm { V } / \mathrm { m } {/tex}

D

{tex} - 200 \mathrm { V } / \mathrm { m } , - 100 \mathrm { V } / \mathrm { m } {/tex}

##### Explanation

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Q 17. A non-conducting radius {tex} 0.5 \mathrm { m } {/tex} carries a total charge {tex} 1.11 \times 10 ^ { - 10 } \mathrm { C } {/tex} distributed non-uniformly on its circumference producing an electric field {tex} \mathrm { E } {/tex} every where in space. The value of the integral {tex} \int _ { \ell = \infty } ^ { \ell = 0 } - \vec { \mathrm { E. }} \vec {\ \mathrm { d }}\ell ( \ell = 0 {/tex} being centre of the ring) in volt is :

{tex} + 2 {/tex}

B

{tex} - 1 {/tex}

C

{tex} - 2 {/tex}

D

Zero

##### Explanation

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Q 18. Two point charges {tex} + q {/tex} and {tex}- q {/tex} are held fixed at {tex}( - d , 0 ){/tex} and {tex}(d, 0 ) {/tex} respectively of a {tex}\mathrm{ x -y}{/tex} coordinate system. Then which of the following statement is incorrect

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

B

No work has to be done in bringing a test charge from {tex} \infty {/tex} to the origin

C

Electric field at all point on {tex} \mathrm { y } {/tex}-axis is parallel to {tex} \mathrm { x } {/tex}-axis

D

The dipole moment is {tex} { 2 } {/tex} qd along the -ve {tex} \mathrm { x } {/tex} -axis

##### Explanation

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Q 19. The work done in rotating an electric dipole of dipole moment p in an electric field {tex}\mathrm E {/tex} through an angle {tex} \theta {/tex} from the direction of electric field, is:

{tex} \mathrm { pE } ( 1 - \cos \theta ) {/tex}

B

{tex} \mathrm { pE } {/tex}

C

zero

D

{tex} - \mathrm { pE } \cos \theta {/tex}

##### Explanation

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Q 20. Which one of the following pattern of electric line of force can't possible:

A

B

D

##### Explanation

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Q 21. Electric flux through a surface of area {tex} 100 \ \mathrm { m } ^ { 2 } {/tex} lying in the xy plane is {tex} ( \mathrm { in } \mathrm { V } - \mathrm { m } ) {/tex} if {tex} \mathrm { E } = \tilde { \mathrm { i } } + \sqrt { 2 } \tilde\mathrm { j } + \sqrt { 3 }\tilde \mathrm { k } {/tex}

A

100

B

141.4

173.2

D

200

##### Explanation

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Q 22. A solid metallic sphere has a charge {tex} + 3 Q . {/tex} Concentric with this sphere is a conducting spherical shell having charge - {tex} Q {/tex}. The radius of the sphere is a and that of the spherical shell is {tex} b ( b > a ) . {/tex} What is the electric field at a distance {tex} R ( a < R < b ) {/tex} from the centre?

A

{tex} \frac { 4 { Q } } { 2 \pi \varepsilon _ { 0 } { R } ^ { 2 } } {/tex}

{tex} \frac { 3 Q } { 4 \pi \varepsilon _ { 0 } R ^ { 2 } } {/tex}

C

{tex} \frac { 3 Q } { 2 \pi \varepsilon _ { R } R ^ { 2 } } {/tex}

D

{tex} \frac { { Q } } { 2 \pi \varepsilon _ { 0 } { R } } {/tex}

##### Explanation

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Q 23. A solid conducting sphere having a charge {tex} Q {/tex} 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 {tex} V {/tex}. If the shell is now given a charge of {tex} - 3 Q , {/tex} the new potential difference between the same two surfaces is :

{tex} V {/tex}

B

{tex} 2 { V } {/tex}

C

{tex} 4 { V } {/tex}

D

{tex} - 2 { V } {/tex}

##### Explanation

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Q 24. A metallic solid sphere is placed in a uniform electric field. The lines of force follow the path(s) shown in figure as :

A

{tex}\mathrm 1{/tex}

B

{tex}\mathrm 2{/tex}

C

{tex}\mathrm 3{/tex}

{tex}\mathrm 4{/tex}

##### Explanation

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Q 25. The electric field intensity at a point at a distance {tex} 2 \mathrm { m } {/tex} from a charge {tex} q {/tex} is {tex} E . {/tex} The amount of work done in bringing a charge of 2 coulomb from infinity to this point will be

A

2{tex} E \mathbf { J } {/tex}

4{tex} E \mathbf { J } {/tex}

C

{tex} \frac { E } { 2 } \mathbf { J } {/tex}

D

{tex} \frac { E } { 4 } \mathbf { J } {/tex}