$A$ charged ball $B$ hangs from a silk thread $S,$ which makes an angle $\theta$ with a large charged conducting sheet $P,$ as shown in the figure. The surface charge density $\sigma$ of the sheet is proportional to $:-$

$A$ spherically symmetric charge distribution is characterized by a charge density $\rho(r) = \rho_0 \left( \frac{5}{4} - \frac{r}{R} \right)$ for $r \le R$ and $\rho(r) = 0$ for $r > R$,where $r$ is the distance from the origin. The electric field at a distance $r$ from the origin $(r < R)$ is given by:

An infinite non-conducting sheet has a surface charge density $\sigma = 0.10 \, \mu C/m^2$ on one side. How far apart are equipotential surfaces whose potentials differ by $50 \, V$?

Two spherical,nonconducting,and very thin shells of uniformly distributed positive charge $Q$ and radius $d$ are located a distance $10d$ from each other. $A$ positive point charge $q$ is placed inside one of the shells at a distance $d/2$ from the center,on the line connecting the centers of the two shells,as shown in the figure. What is the net force on the charge $q$?

$A$ long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral. Then

The electric field intensity at $P$ and $Q$,in the shown arrangement,are in the ratio: