Electrostatics

A large conducting slab having uniform surface charge density is placed between a parallel plate capacitor as shown in the figure. The net surface charge density on the slab after its placement in between the capacitor…

A bead of mass $m$ and charge $-q$ is constrained to move along a line. A charge of $+Q$ is kept at $d$ distance away from the line as shown in the figure. The charged bead is released from rest at a point far away from…

A hollow thin-walled glass tube of length $L$, is open at one end while the other end is closed by a hollow thin-walled glass hemisphere of radius $R$. The axis of the tube is along the $x$-axis with the open end at the…

Three point charges are arranged in the $x-y$ plane as shown in the figure. Assuming that the potential at the infinity is zero, the approximate potential at the point P in the figure is

A long wire with a uniform linear charge density $\lambda$ is placed along the common axis of two long coaxial thin cylindrical shells of radii $R_1$ and $R_2$ (see figure). The outer shell carries a uniform surface…

Consider a parallel plate capacitor filled with a dielectric of relative permittivity 2 . One of the plates has charge density $+\sigma$ while other has charge density $-\sigma$. Assume that the points are not too near…

An electrostatic field line leaves at an angle $\alpha$ from point charge $q_1$, and connects with point charge $-q_2$ at an angle $\beta$ ($q_1$ and $q_2$ are positive), as shown schematically in the figure. We have…

Two positive equal charges are placed symmetrically about the origin on the $x$-axis and kept fixed as shown. Another positive charge $Q$ is placed at the origin. The charge $Q$ can be displaced by a very small distance…

The variation of the magnitude of the electric field with radial distance $r$ due to a given configuration is depicted in the accompanying figure. The configuration could be

A positive point charge $q$ is placed near a three dimensional isolated, neutral solid conductor with a cavity as shown. The possible electric lines of force are best depicted in:

A circular loop of radius $a$, centered at origin has five positive charges equally spaced on it. All charges have a magnitude Q , except the one at $(0, a)$ which has a magnitude $q$, as shown in the figure. The…

A uniformly charged sphere, of total charge $Q$, is expanding uniformly about its center. The magnitude of the electric field $E$ at a point $r$ from the center of the sphere as a function of radius of the sphere varies…