List of top Physics Questions on Electrostatics asked in JEE Advanced

Consider an electric dipole comprising two charges $+q$ and $-q$, each with mass $m$, separated by a fixed distance $d$ and initially at rest with its dipole moment pointing along $\hat{i}$. A uniform electric field $E\hat{j}$ is turned on at time $t=0$ and it is turned off at $t=t_f$, when the dipole moment makes an angle $\theta_f$ with $\hat{i}$. Neglecting any sources of energy loss, correct option(s) is/are:

Two charges $Q_1 = q$ and $Q_2 = mq$ are placed at the points $P_1(a, b)$ and $P_2(ma, mb)$, respectively, in the $XY$ plane, where $a, b \neq 0$ and $m \neq 0, 1$. If $V_1$ is the potential at a point in the $XY$ plane due to charge $Q_1$ and $V_2$ is the potential at that point due to charge $Q_2$. Correct statement(s) for the points at which $|V_1| = |V_2|$ is/are:

Two co-axial conducting cylinders of same length $ \ell $ with radii $ \sqrt{2}R $ and $ 2R $ are kept, as shown in Fig. 1. The charge on the inner cylinder is $ Q $ and the outer cylinder is grounded. The annular region between the cylinders is filled with a material of dielectric constant $ \kappa = 5 $. Consider an imaginary plane of the same length $ \ell $ at a distance $ R $ from the common axis of the cylinders. This plane is parallel to the axis of the cylinders. Ignoring edge effects, the flux of the electric field through the plane is $ (\varepsilon_0 \text{ is the permittivity of free space}) $:

A positive point charge of $10^{-8}$ C is kept at a distance of 20 cm from the center of a neutral conducting sphere of radius 10 cm. The sphere is then grounded and the charge on the sphere is measured. The grounding is then removed and subsequently the point charge is moved by a distance of 10 cm further away from the center of the sphere along the radial direction. Taking $ \frac{1}{4\pi\varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2/\text{C}^2 $, which of the following statements is/are correct:

Six infinitely large and thin non-conducting sheets are fixed in configurations I and II. As shown in the figure, the sheets carry uniform surface charge densities which are indicated in terms of $\sigma_0$. The separation between any two consecutive sheets is $1 \, \mu m$. The various regions between the sheets are denoted as 1, 2, 3, 4 and 5. If $\sigma_0 = 9 \, \mu C/m^2$, then which of the following statements is/are correct? (Take permittivity of free space $\epsilon_0 = 9 \times 10^{-12} \, \text{F/m}$)

List-I shows four configurations, each consisting of a pair of ideal electric dipoles. Each dipole has a dipole moment of magnitude $ p $, oriented as marked by arrows in the figures. In all the configurations the dipoles are fixed such that they are at a distance $ 2r $ apart along the $ x $-direction. The midpoint of the line joining the two dipoles is $ X $. The possible resultant electric fields $ \vec{E} $ at $ X $ are given in List-II. Choose the option that describes the correct match between the entries in List-I to those in List-II.

Two coaxial cylinders have radii $\sqrt{2}R$ and $2R$, with a rectangular plane placed parallel to their common axis. If the electric field exists in the space between the cylinders with dielectric constant $K = 5$, find the total electric flux through the rectangular plane that lies in this region.

A container has a base of 50 cm × 5 cm and height 50 cm, as shown in the figure. It has two parallel electrically conducting walls each of area 50 cm × 50 cm. The remaining walls of the container are thin and non-conducting. The container is being filled with a liquid of dielectric constant 3 at a uniform rate of 250 cm3s−1. What is the value of the capacitance of the container after 10 seconds? [Given: Permittivity of free space 𝜖0 = 9 × 10−12 C2N−1m−2, the effects of the non-conducting walls on the capacitance are negligible]

A point charge $q$ of mass $m$ is suspended vertically by a string of length $1$. A point dipole of dipole moment $\vec{ p }$ is now brought towards $q$ from infinity so that the charge moves away. The final equilibrium position of the system including the direction of the dipole, the angles and distances is shown in the figure below. If the work done in bringing the dipole to this position is $N \times( mgh )$, where $g$ is the acceleration due to gravity, then the value of $N$ is_______ .
(Note that for three coplanar forces keeping a point mass in equilibrium, $\frac{F}{\sin \theta}$ is the same for all forces, where $F$ is any one of the forces and $\theta$ is the angle between the other two forces)

Two identical non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting, massless strings of same length. At equilibrium, the angle between the strings is $\alpha$. The spheres are now immersed in a dielectric liquid of density $800\, kg \,m ^{-3}$ and dielectric constant $21$. If the angle between the strings remains the same after the immersion, then