Electrostatic Potential Energy

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LEVELJEE Main

The question contains Statement I and Statement II. Of the four choices given after the statements, choose the one that best describes the two statements. Statement I For a charged particle moving from point $P$ to point $Q$ , the net work done by an electrostatic field on the particle is independent of the path connecting point $P$ to point $Q$ . Statement II The net work done by a conservative force on an object moving along a closed loop is zero.

(A)

Statement I is true, Statement II is false

(B)

Statement I is true, Statement II is true; Statement II is not the correct explanation of Statement I

(C)

Statement I is true, Statement II is true; Statement II is the correct explanation of Statement I

(D)

Statement I is false, Statement II is true

JEE Main 2020

LEVELJEE Advanced

A solid sphere of radius $R$ carries a charge $Q + q$ distributed uniformly over its volume. A very small point-like piece of it of mass $m$ gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge $q$ . If it acquires a speed $v$ when it has fallen through a vertical height $y$ (see figure), then (Assume the remaining portion to be spherical.)

(A)

v^{2} = y [\frac{q Q}{4 π ϵ _{0} R ^{2} y m} + g]

(B)

v^{2} = 2 y [\frac{q Q}{4 π ϵ _{0} R ( R + y ) m} + g]

(C)

v^{2} = y [\frac{q Q}{4 π ϵ _{0} R ( R + y ) m} + g]

(D)

v^{2} = 2 y [\frac{q QR}{4 π ϵ _{0} ( R + y ) ^{3} m} + g]

JEE Advanced 1992

LEVELJEE Advanced

(a) If the same charge of $Q$ as in part (a) above is given to a spherical conductor of the same radius $R$ , what will be the energy of the system? (b) A charge of $Q$ is uniformly distributed over a spherical volume of radius $R$ . Obtain an expression for the energy of the system. Assume the earth to be a sphere of uniform mass density. Calculate this energy, given the product of the mass and the radius of the earth to be $2.5 \times 1 0^{31} kg-m$ . (c) What will be the corresponding expression for the energy needed to completely disassemble the planet earth against the gravitational pull amongst its constituent particles?

JEE Advanced 1985

LEVELJEE Advanced

Two fixed, equal, positive charges, each of magnitude $q = 5 \times 1 0^{- 5} C$ are located at points $A$ and $B$ separated by a distance of 6 m. An equal and opposite charge moves towards them along the line $C O D$ , the perpendicular bisector of the line $A B$ . The moving charge, when reaches the point $C$ at a distance of 4 m from $O$ , has a kinetic energy of 4 J. Calculate the distance of the farthest point $D$ which the negative charge will reach before returning towards $C$ .

LEVELJEE Main

Two equal point charges are fixed at $x = - a$ and $x = + a$ on the x-axis. Another point charge $Q$ is placed at the origin. The change in the electrical potential energy of $Q$ , when it is displaced by a small distance $x$ along the x-axis, is approximately proportional to

(A)

x

(B)

x^{2}

(C)

x^{3}

(D)

1/ x

JEE Advanced 2003

LEVELJEE Advanced

Eight point charges are placed at the corners of a cube of edge $a$ as shown in figure. Find the work done in disassembling this system of charges.

JEE Advanced 2011

LEVELJEE Advanced

Four point charges, each of $+ q$ , are rigidly fixed at the four corners of a square planar soap film of side $a$ . The surface tension of the soap film is $γ$ . The system of charges and planar film are in equilibrium, and $a = k [\frac{q ^{2}}{γ}]^{1/ N}$ , where $k$ is a constant. Then $N$ is

JEE Main 2019

LEVELJEE Main

In free space, a particle $A$ of charge $1 μ C$ is held fixed at a point $P$ . Another particle $B$ of the same charge and mass $4 μ g$ is kept at a distance of $1 mm$ from $P$ . If $B$ is released, then its velocity at a distance of $9 mm$ from $P$ is $[Take, \frac{1}{4 π ε _{0}} = 9 \times 1 0^{9} N-m^{2} C^{- 2}]$

(A)

1.5 \times 1 0^{2} m/s

(B)

3.0 \times 1 0^{4} m/s

(C)

1.0 m/s

(D)

2.0 \times 1 0^{3} m/s

JEE Main 2019

LEVELJEE Advanced

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 π ϵ _{0}} [- \frac{q ^{2}}{d} + \frac{2 q Q d}{D ^{2}}]

(B)

\frac{1}{4 π ϵ _{0}} [+ \frac{q ^{2}}{d} + \frac{q Q d}{D ^{2}}]

(C)

\frac{1}{4 π ϵ _{0}} [- \frac{q ^{2}}{d} - \frac{q Q d}{2 D ^{2}}]

(D)

\frac{1}{4 π ϵ _{0}} [- \frac{q ^{2}}{d} - \frac{q Q d}{D ^{2}}]

JEE Main 2019

LEVELJEE Main

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)

- 2 q

(B)

\frac{- q}{1 + 2}

(C)

+ q

(D)

\frac{- 2 q}{2 + 1}

JEE Main 2021

LEVELJEE Main

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.

LEVELJEE Main

A charged particle $q$ is shot towards another charged particle $Q$ which is fixed with a speed $v$ . It approaches $Q$ upto a closest distance $r$ and then returns. If $q$ was given a speed $2 v$ , the closest distance of approach would be

(A)

r

(B)

2 r

(C)

\frac{r}{2}

(D)

\frac{r}{4}

LEVELJEE Main

Two positive charges of magnitude $q$ are placed at the ends of a side 1 of a square of side $2 a$ . Two negative charges of the same magnitude are kept at the other corners. Starting from rest, if a charge $Q$ moves from the middle of side 1 to the centre of square, its kinetic energy at the centre of square is

(A)

\frac{1}{4 π ϵ _{0}} \frac{2 q Q}{a} (1 - \frac{1}{5})

(B)

zero

(C)

\frac{1}{4 π ϵ _{0}} \frac{2 q Q}{a} (1 + \frac{1}{5})

(D)

\frac{1}{4 π ϵ _{0}} \frac{2 q Q}{a} (1 - \frac{2}{5})

JEE Main 2020

LEVELJEE Advanced

Two point charges $4 q$ 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 semi-circle as shown in the figure, the energy of the charge will

(A)

increase by

\frac{2 q ^{2}}{3 π ε _{0} d}

(B)

decrease by

\frac{4 q ^{2}}{3 π ε _{0} d}

(C)

increase by

\frac{3 q ^{2}}{4 π ε _{0} d}

(D)

decrease by

\frac{q ^{2}}{4 π ε _{0} d}

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Eight point charges are placed at the corners of a cube of edge a as shown in figure. Find the work done in disassembling this system of charges.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } 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

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.

Eight point charges are placed at the corners of a cube of edge $a$ as shown in figure. Find the work done in disassembling this system of charges.

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