Electrostatics Practice Questions

Two point charges 8μC and -2μC are located at x = 2 cm and x = 4 cm, respectively on the x-axis. The ratio of electric flux due to these charges through two spheres of radii 3 cm and 5 cm with their centers at the origin is________.[JEE Main 2 apr 2026 Shift 2]

A three coulomb charge moves from the point (0, -2, -5) to the point (5, 1, 2) in an electric field expressed as ${ \vec{\text{E}}}=2 x { {\text{i}}}^{∧}+3 {\text{y}}^{2} { {\text{j}}}^{∧}+4 { {\text{k}}}^{∧} {\text{N}} / {\text{C}}$. The work done in moving the charge is ________ J.[JEE Main 6 Apr 2026 shift 1]

Consider two identical metallic spheres of radius $R$ each having charge $Q$ and mass $m$. Their centers have an initial separation of $4 R$. 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 $k=\;\frac{1}{4 \pi E_0}$ and assume $k Q^2>G m^2$ where $G$ is the Gravitational constant)

Two point charges ${\text{q}}_{1}=3 \mu {\text{C}}$ and ${\text{q}}_{2}=-4 \mu {\text{C}}$ are placed at points $(2 {i}^{∧}+3 {j}^{∧}+3 {k}^{∧})$ and $({i}^{∧}+{j}^{∧}+{k}^{∧})$ respectively. Force on charge $q_2$ is _________ N.$(Take \;\frac{1}{4 \pi E_{0}}=9 \times 10^{9}\, SI\ Units)$[JEE Main 8 apr 2026 shift 2]

Electric charge is transferred to an irregular metallic disk as shown in figure. If $\sigma _1, \sigma _2, \sigma _3$ and $\sigma _4$ are charge densities at given points then, choose the correct answer from the options given below: A. $\sigma _1>\sigma _3 ; \sigma _2=\sigma _4$ B. $\;\; \sigma _1>\sigma _2 ; \sigma _3>\sigma _4$ C. $\sigma _1>\sigma _3>\sigma _2=\sigma _4$ D. $\sigma _1< \sigma _3< \sigma _2=\sigma _4$ E. $\sigma _1=\sigma _2=\sigma _3=\sigma _4$

The electric field in a region is given by $\vec{E}=(2 {i}^{∧}+4 {j}^{∧}+6 {k}^{∧}) \times 10^3 {\text{N}} / {\text{C}}$. The flux of the field through a rectangular surface parallel to $x-z$ plane is $6.0 {\text{Nm}}^2 {\text{C}}^{-1}$. The area of the surface is $\_\_\_\_$ ${\text{cm}}^2$.

An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density $\sigma _0$. Choose the correct option from the following.

Two infinite identical charged sheets and a charged spherical body of charge density ' $\rho$ ' are arranged as shown in figure. Then the correct relation between the electrical fields at $A, B, C$ and $D$ points is

A line charge of length ' $\;\frac{a}{2}$ ' is kept at the center of an edge $B C$ of a cube $A B C D E F G H$ having edge length ' $a$ ' as shown in the figure. If the density of line charge is $\lambda C$ per unit length, then the total electric flux through all the faces of the cube will be ______ (Take, $\epsilon _0$ as the free space permittivity)

A point particle of charge $Q$ is located at $P$ along the axis of an electric dipole 1 at a distance $r$ as shown in the figure. The point $P$ is also on the equatorial plane of a second electric dipole 2 at a distance $r$. The dipoles are made of opposite charge $q$ separated by a distance $2 a$. For the charge particle at $P$ not to experience any net force, which of the following correctly describes the situation?

A point charge causes an electric flux of $-2 \times 10^4$ ${\text{Nm}}^2 {\text{C}}^{-1}$ to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is: (Given $E_0=8.85 \times 10^{-12} {\text{C}}^2 {\text{N}}^{-1} {\text{m}}^{-2}$ )

Consider a circular loop that is uniformly charged and has a radius $a {\sqrt{2}}$. Find the position along the positive $z$-axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in $x y$ plane at the origin

List-I List-II (A) Electric field inside (distance $r>0$ from center) of a uniformly charged spherical shell with surface charge density $\sigma$, and radius $R$. (I) $\sigma / \epsilon _0$ (B) Electric field at distance $r>0$ from a uniformly charged infinite plane sheet with surface charge density $\sigma$. (II) $\sigma / 2 \epsilon _0$ (C) Electric field outside (distance $r>0$ from center) of a uniformly charged spherical shell with surface charge density $\sigma$, and radius $R$. (III) 0 (D) Electric field between oppositely charged infinite plane parallel sheets with uniform surface charge density $\sigma$. (IV) $\;\frac{\sigma }{\epsilon _0 r^2}$ Choose the correct answer from the options given below:

If $E_0$ denotes the permittivity of free space and $\varphi _E$ is the flux of the electric field through the area bounded by the closed surface, then dimensions of $(E_0 \;\frac{d \varphi _E}{d t})$ are that of:

Consider a parallel plate capacitor of area $A$ (of each plate) and separation ' $d$ ' between the plates. If $E$ is the electric field and $\epsilon _0$ is the permittivity of free space between the plates, then potential energy stored in the capacitor is

Two small spherical balls of mass 10 g each with charges $-2 \mu {\text{C}}$ and $2 \mu {\text{C}}$, are attached to two ends of very light rigid rod of length 20 cm . The arrangement is now placed near an infinite nonconducting charge sheet with uniform charge density of $100 \mu {\text{C}} / {\text{m}}^2$ such that length of rod makes an angle of $30^{\circ}$ with electric field generated by charge sheet. Net torque acting on the rod is: (Take $\epsilon _0=8.85 \times 10^{-12} {\text{C}}^2 / {\text{Nm}}^2$ )

A dipole with two electric charges of $2 \mu {\text{C}}$ magnitude each, with separation distance $0.5 \mu {\text{m}}$, is placed between the plates of a capacitor such that its axis is parallel to an electric field established between the plates when a potential difference of 5 V is applied. Separation between the plates is 0.5 mm . If the dipole is rotated by $30^{\circ}$ from the axis, it tends to realign in the direction due to a torque. The value of torque is :

A metallic ring is uniformly charged as shown in figure. $A C$ and $B D$ are two mutually perpendicular diameters. Electric field due to ${\text{arc}} A B$ at ' $O$ ' is ' $E$ ' in magnitude. What would be the magnitude of electric field at ' $O$ ' due to arc $A B C$ ?