Electrostatic Potential Energy

Three equal $(+q)$ charges are placed in air at the vertices of equilateral triangle. If the side of equilateral triangle is $l$, the net potential energy of the system is $\left[K = \frac{1}{4\pi\epsilon_0}\right]$

A charge $10\ \mu\text{C}$ exists at the centre of a square. The work done in moving a $2\ \mu\text{C}$ point charge from corner A to corner B of a square ABCD is

If $100$ J of work has to be done in moving an electric charge of $4$ C from a place, where potential is $-10$ V to another place where potential is V volt. The value of V is

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 $\underline{\qquad}\ \mu\text{J}$.

$\frac{1}{4\pi\epsilon_0} = 9 \times 10^{9}\text{ N}\cdot\text{m}^2/\text{C}^2$

A point charge of $10^{-8}\text{ C}$ is placed at origin. The work done in moving a point charge $2\ \mu\text{C}$ from point $A(4, 4, 2)\text{ m}$ to $B(2, 2, 1)\text{ m}$ is ______ J. $(\frac{1}{4\pi\epsilon_0} = 9 \times 10^{9}$ in SI units)

Two charges of equal magnitude '$q$' are placed in air at a distance '$2a$' apart and third charge $-2q$ is placed at mid-point. The potential energy of the system is ($\epsilon_0$ = permittivity of free space)

The equal charges (say 'q') are placed at a distance of $4r$ and a third charge $(-2q)$ is placed at a mid-point. The potential energy of the system is ($\epsilon_0 =$ permittivity of free space)

Two equal positive charges each of value 'q' are placed at points A and B, where $AB = 3x$. A third charge $-3q$ is placed at point C at a distance $x$ from A on AB. The potential energy of the system is nearly ($\epsilon_0$ = permittivity of free space)

Three point charges Q, $+2q$ and $+q$ are placed at the vertices of a right-angled isosceles triangle of length $\sqrt{2}a$ as shown in figure. The net electrostatic potential energy of the configuration is zero, if Q is equal to

Three point charges +q, +2q and +Q are placed at the vertices of an equilateral triangle. If the potential energy of the system of three charges is zero, the value of Q in terms of q is

Two charges $q_1$ and $q_2$ are separated by a distance of 30cm. A third charge $q_3$ initially at point C is shown in 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 $q_3k/4\pi\varepsilon_0$, the value of K is ($\varepsilon_0$ = permittivity of free space)

Two point charges $q_1 = 6\,\mu$C and $q_2 = 4\,\mu$C are kept at points A and B in air where distance $AB = 10$ cm. What is the increase in potential energy of the system when $q_2$ is moved towards $q_1$, by 2 cm? $\Bigg(\frac{1}{4\pi\epsilon_0} = 9 \times 10^{9}$ SI units$\Bigg)$

Two charges $7\mu\text{C}$ and $-2\mu\text{C}$ are placed at $(-9, 0, 0)\text{ cm}$ and $(9, 0, 0)\text{ cm}$ respectively in an external field $E = \frac{A}{r^2}\hat{r}$, where $A = 9 \times 10^{5}\text{ N/C}\cdot\text{m}^2$. Considering the potential at infinity is 0, the electrostatic energy of the configuration is ______ J.

Three point charges $+q, -2q$ and $-2q$ are placed at the vertices of an equilateral triangle of side a. The work done by some external force to increase their separation to '$2a$' will be $\left(K = \frac{1}{4\pi\varepsilon_0}\right)$

A particle of mass 'm' and charge 'q', initially at rest, is accelerated by a uniform electric field 'E' through a distance 'D' and is then allowed to approach a fixed static charge 'Q' of the same sign. The distance of the closest approach of the charge q is

[ $\epsilon_0$ = permittivity of free space ]

A three coulomb charge moves from the point $(0, -2, -5)$ to the point $(5, 1, 2)$ in an electric field expressed as $\vec{E} = 2x\hat{i} + 3y^2\hat{j} + 4\hat{k}\text{ N/C}$. The work done in moving the charge is ______ J.

In air, a charged soap bubble of radius R breaks in to 27 small soap bubbles of equal radii r. Then the ratio of mechanical force acting per unit area of big soap bubble to that of a small soap bubble is

Consider a fixed uniformly charged insulating sphere with radius $R$ and total charge $+Q$. A point charge $-q$ ( $q \ll Q$) with mass $m$ is released from rest at a distance of $3R$ from the centre of the charged sphere. When the point charge reaches the surface of the sphere, its speed is: ( $\varepsilon_0$ is the permittivity of vacuum, neglect gravitational forces).

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 $k = \frac{1}{4\pi\epsilon_0}$ and assume $kQ^2 > Gm^2$ where $G$ is the Gravitational constant)

An uniformly charged thin spherical shell of radius 'R' has uniform surface charge density '$\sigma$'. It is made of two hemispherical identical shells held together by pressing them with force 'F' as shown. F is proportional to

[$\epsilon_0$ = permittivity of free space]

Two charges $7\ \mu\text{C}$ and $-4\ \mu\text{C}$ are placed at $(-7\text{ cm}, 0, 0)$ and $(7\text{ cm}, 0, 0)$ respectively. Given, $\epsilon_0 = 8.85 \times 10^{-12}\text{ C}^2\text{ N}^{-1}\text{ m}^{-2}$, the electrostatic potential energy of the charge configuration is:

Let ' $W$ ' joule be the work done to move an electric charge ' $q$ ' coulomb from a place $A$, where potential is -5 volt to another place $B$ where potential is ' $V$ ' volt. The value of ' $V$ ' is

Three charges $Q, (-2q)$ and $(-2q)$ are placed at the vertices of an isosceles right angled triangle as shown in figure. The net electrostatic potential energy is zero if $Q$ is equal to

Three charges each of magnitude $3\mu\text{C}$, are placed on the vertices of an equilateral triangle of side 6 cm. The net potential energy of the system will be nearly $\Bigg[\frac{1}{4\pi\epsilon_0} = 9 \times 10^{9}$ SI unit $\Bigg]$

Three point charges $+Q, +2Q$ and $q$ are placed at the vertices of an equilateral triangle. The value of charge $q$ in terms of $Q$, so that electrical potential energy of the system is zero, is given by

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 $\frac{q_3 K}{4\pi\epsilon_0}$, the value of K is:

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 square of side length ' $a$ '. In the second configuration (2), the same charges are shifted to mid points $G, E, H$ and $F$, of the square. If $K = \frac{1}{4\pi\epsilon_0}$, the difference between the potential energies of configuration (2) and (1) is given by:

Two point charges $+10\mu\text{C}$ and $4\mu\text{C}$ are placed 10 cm apart in air. The work required to be done to bring them 2 cm closer is

$\Bigg(\frac{1}{4\pi\varepsilon_0} = 9 \times 10^{9}$ SI units $\Bigg)$

If a unit positive charge is shifted from a region of low potential to a region of high potential, then the electric potential energy of the system

In an electric field due to charge $Q$, a charge $q$ moves from point A to B as shown in the figure. The work done is ( $\varepsilon_0 =$ permittivity of free space)

If a $10\ \mu\text{C}$ charge exists at the centre of a square, the work done in moving a $2\ \mu\text{C}$ point charge from corner A to corner B of a square ABCD is

90 J of work is done to move an electric charge of magnitude 3 C from a place A, where potential is -10 V to another place B, where potential is ' $V_1$ ' volt. The value of $V_1$ is

Two point charges $q_1 = 6\mu\text{C}$ and $q_2 = 4\mu\text{C}$ are kept at points $A$ and $B$ in air where $AB = 10\text{ cm}$. What is the increase in potential energy of the system when $q_2$ is moved towards $q_1$ by 2 cm? $\Bigg(\frac{1}{4\pi\varepsilon_0} = 9 \times 10^{9}$ SI units $\Bigg)$

Three charges are placed at the vertices of an equilateral triangle as shown in the figure. For what value of charge ' $Q$ ', the electrostatic potential energy of the system is zero?

Two charged particles each having charge ' $q$ ' and mass ' $m$ ' are held at rest while their separation is ' $r$ '. The speed of the particles when their separation is ' $\frac{r}{2}$ ' will be ( $\varepsilon_0 =$ permittivity of the medium)

In the electric field due to a charge $Q$, a charge $q$ moves from point $A$ to $B$. The work done is ( $\varepsilon_0 =$ permittivity of vacuum)

A point charge $2 \times 10^{-2}\text{ C}$ is moved from P to S in a uniform electric field of $30\text{ N C}^{-1}$ directed along positive x-axis. If coordinates of P and S are (1, 2, 0) m and (0, 0, 0) m respectively, the work done by electric field will be

Two point charges '$q_1$ ' and '$q_2$' are separated by a distance '$d$'. What is the increase in potential energy of the system when '$q_2$' is moved towards '$q_1$' by a distance '$x$'? $(x < d)\ (\frac{1}{4\pi\varepsilon_0} = K$, constant)

Three point charges $+Q, +2q$ and $+q$ are placed at the vertices of a right angled isosceles triangle. The net electrostatic potential energy of the configuration is zero, if $Q$ is equal to

Two charges of equal magnitude '$q$' are placed in air at a distance '$2r$' apart and third charge '$-2q$' is placed at mid point. The potential energy of the system is $(\varepsilon_0 =$ permittivity of free space)

Three point charges $+q, +2q$ and $+Q$ are placed at the three vertices of an equilateral triangle. If the potential energy of the system of three charges is zero, the value of $Q$ in terms of $q$ is

Three charges each of value $+q$ are placed at the corners of an isosceles triangle $ABC$ of sides $AB$ and $AC$ each equal to $2a$. The mid points of $AB$ and $AC$ are $D$ and $E$ respectively. The work done in taking a charge $Q$ from $D$ to $E$ is ( $\varepsilon_0 =$ permittivity of free space)

Six charges +q, $-$q, +q, $-$q, +q, and $-$ q are fixed at the corners of a hexagon of side d as shown in the figure. The work done in bringing a charge q0 to the centre of the hexagon from infinity is ($\varepsilon_0$ - permittivity of free space)

Eight similar drops of mercury are maintained at 12 V each. All these spherical drops combine into a single big drop. The potential energy of bigger drop will be ____________ E. Where E is the potential energy of a single smaller drop.

Three charges $-q, Q$ and $-q$ are placed at equal distances on a straight line. If the total potential energy of the system of three charges is zero then the ratio $\frac{Q}{q}$ is

27 similar drops of mercury are maintained at 10V 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.

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 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 system of three charges are placed as shown in the figure:

If D >> d, the potential energy of the system is best given by:

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:

In free space, a particle A of charge 1$\mu$C is held fixed at a point P. Another particle B of the same charge and mass 4$\mu$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: $\left[\text{Take } \frac{1}{4\pi\epsilon_0} = 9 \times 10^{9}\text{ Nm}^2\text{C}^{-2}\right]$

A positive point charge is released from rest at a distance r0 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 :-

Four equal point charges Q each are placed in the xy plane at (0, 2), (4, 2), (4, –2) and (0, –2). The work required to put a fifth charge Q at the origin of the coordinate system will be -

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

There is a uniform spherically symmetric surface charge density at a distance R0 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:

Three charges, each +q, are placed at the corners of an isosceles triangle ABC of sides BC and AC, 2$a$. D and E are the mid points of BC and CA. The work done in taking a charge Q from D to E is

Two points $P$ and $Q$ are maintained at the potentials of $10\text{ V}$ and $-4\text{ V}$, respectively. The work done in moving $100$ electrons from $P$ to $Q$ is:

Charges +q and $-$ q are placed at points A and B respectively which are a distance 2L apart, C is the midpoint between A and B. The work done in moving a charge + Q along the semicircle CRD is

As per the diagram a point charge +q is placed at the origin O. Work done in taking another point charge $-$ Q from the point A [coordinates (0, $a$)] to another point B

Two charges q1 and q2 are placed 30 cm apart, as shown in the figure. A third charge q3 is moved along the arc of a circle of radius 40 cm from C to D.

The change in the potential energy of the system is $\frac{q_3}{4\pi\varepsilon_0}k$ where k is

A bullet of mass 2 g is having a charge of 2 $\mu$C. Through what potential difference must it be accelerated, starting from rest, to acquire a speed of 10 m/s?

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 $q$ were given a speed of $2v$ the closest distance of approach would be

Identical charges ($-$q) are placed at each corners of cube of side b then electrostatic potential energy of charge (+q) which is placed at centre of cube will be

In bringing an electron towards another electron, the electrostatic potential energy of the system

When a proton is accelerated through $1\text{ V}$ its kinetic energy will be

There is an electric field $E$ in $x$-direction. If the work done on moving a charge of $0.2\text{ C}$ through a distance of $2\text{ m}$ along a line making an angle $60^\circ$ with $x$-axis is $4\text{ J}$, then what is the value of $E$?

Charge $q_2$ is at the centre of a circular path with radius $r$. Work done in carrying charge $q_1$, once around this equipotential path, would be