List of top Physics Questions on Electrostatics asked in JEE Main, Vellore Institute of Technology Engineering Entrance Examination

Assertion (A): Work done to move a charge between two points is zero inside a uniformly charged shell.
Reason (R): Potential inside a uniformly charged shell is constant and equal to the potential at its surface.

Given $\lambda = \frac{2nc}{m}$ (linear charge density) for a wire which is passing through the body diagonal of a closed cube of side length $\sqrt{3}$ cm. Find the flux through the cube.

There are two charged spheres of radius $R$ and $3R$. When the spheres are made to touch each other and then separate, the surface charge density becomes $r_1$ and $r_2$ respectively. Find $\frac{r_1}{r_2}$.

For a short dipole placed at origin \( O \), the dipole moment \( P \) is along the \( x \)-axis, as shown in the figure. If the electric potential and electric field at \( A \) are \( V_0 \) and \( E_0 \) respectively, then the correct combination of the electric potential and electric field, respectively, at point \( B \) on the \( y \)-axis is given by: 

Three capacitors of capacitances 25 μF, 30 μF and 45 μF are connected in parallel to a supply of 100 V. Energy stored in the above combination is E. When these capacitors are connected in series to the same supply, the stored energy is \(\frac{9}{x} E\)  . The value of x is .................

The electric field between the two parallel plates of a capacitor of 1.5 μF capacitance drops to one third of its initial value in 6.6 μs when the plates are connected by a thin wire. The resistance of this wire is .............. Ω. (Given, log 3 = 1.1)

In a co-axial straight cable, the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero.

If the net electric field at point \( P \) along \( Y \)-axis is zero, then the ratio of \[ \left| \frac{q_2}{q_3} \right| \] is \[\frac{8}{5\sqrt{x}},\] where \( x = \dots \dots \dots \dots \dots \).

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle θ with each other. When suspended in water the angle remains the same. If density of the material of the sphere is 1.5 g/cc, the dielectric constant of water will be ________ (Take density of water = 1 g/cc)

A parallel plate capacitor with plate separation 5mm is charged up by a battery. It is found that on introducing a dielectric sheet of thickness 2 mm, while keeping the battery connections intact, the capacitor draws 25% more charge from the battery than before. The dielectric constant of the sheet is ____.

Two charges \( q \) and \( 3q \) are separated by a distance \( r \) in air. At a distance \( x \) from charge \( q \), the resultant electric field is zero. The value of \( x \) is:

A capacitor has air as dielectric medium and two conducting plates of area \(12 \, \text{cm}^2\) and they are \(0.6 \, \text{cm}\) apart. When a slab of dielectric having area \(12 \, \text{cm}^2\) and \(0.6 \, \text{cm}\) thickness is inserted between the plates, one of the conducting plates has to be moved by \(0.2 \, \text{cm}\) to keep the capacitance same as in previous case. The dielectric constant of the slab is:
\((\text{Given } \epsilon_0 = 8.834 \times 10^{-12} \, \text{F/m})\)

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 37° with each other. When suspended in a liquid of density 0.7 g/cm³, the angle remains the same. If the density of the material of the sphere is 1.4 g/cm³, the dielectric constant of the liquid is ___________. (tan 37° =\( \frac{3}{4}\))

An infinite plane sheet of charge having uniform surface charge density \( +\sigma_s \, \text{C/m}^2 \) is placed on the \( x \)-\( y \) plane. Another infinitely long line charge having uniform linear charge density \( +\lambda_e \, \text{C/m} \) is placed at \( z = 4 \, \text{m} \) plane and parallel to the \( y \)-axis. If the magnitude values \( |\sigma_s| = 2 |\lambda_e| \), then at point \( (0, 0, 2) \), the ratio of magnitudes of electric field values due to sheet charge to that of line charge is \( \pi \sqrt{n} : 1 \).The value of \( n \) is ______.

An infinitely long positively charged straight thread has a linear charge density \( \lambda \, \text{Cm}^{-1} \). An electron revolves along a circular path having its axis along the length of the wire. The graph that correctly represents the variation of the kinetic energy of the electron as a function of the radius of the circular path from the wire is:

An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet \( S \) having surface charge density \( +\sigma \). The electron at \( t = 0 \) is at a distance of 1 m from \( S \) and has a speed of 1 m/s. The maximum value of \( \sigma \) if the electron strikes \( S \) at \( t = 1 \, \text{s} \) is \( \alpha \left[ \frac{m \epsilon_0}{e} \right] \frac{\text{C}}{\text{m}^2} \). The value of \( \alpha \) is ______.

Two charges of \( -4 \, \mu C \) and \( +4 \, \mu C \) are placed at the points \( A(1, 0, 4) \, m \) and \( B(2, -1, 5) \, m \) located in an electric field \( \vec{E} = 0.20 \, \hat{i} \, V / cm \). The magnitude of the torque acting on the dipole is \( 8\sqrt{\alpha} \times 10^{-5} \, Nm \), where \( \alpha = \, \).

Given below are two statements : one is labelled a Assertion (A) and the other is labelled as Reason(R)
Assertion (A) : Work done by electric field on moving a positive charge on an equipotential surface is always zero.
Reason (R) : Electric lines of forces are always perpendicular to equipotential surfaces.
In the light of the above statements, choose the most appropriate answer from the options given below :

A thin metallic wire having a cross-sectional area of \( 10^{-4} \, \text{m}^2 \) is used to make a ring of radius 30 cm. A positive charge of \( 2\pi \, C \) is uniformly distributed over the ring, while another positive charge of 30 pC is kept at the center of the ring. The tension in the ring is ______ N; provided that the ring does not deform (neglect the influence of gravity).
(Given, \(\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{SI units}\))

Three infinitely long charged thin sheets are placed as shown in the figure. The magnitude of the electric field at the point \( P \) is \(\frac{x \sigma}{\epsilon_0}\). The value of \( x \) is _________.
(All quantities are measured in SI units).