$A$ hollow insulated conducting sphere is given a positive charge of $10\,\mu C$. What will be the electric field at the centre of the sphere if its radius is $2\,m$?

$A$ cube of side $a$ is placed in an electric field $\vec{E} = E_0 x \hat{i}$. What is the total charge enclosed by the cube?

Consider the force $F$ on a charge $q$ due to a uniformly charged spherical shell of radius $R$ carrying charge $Q$ distributed uniformly over it. Which one of the following statements is true for $F$,if $q$ is placed at distance $r$ from the centre of the shell?

If an insulated non-conducting sphere of radius $R$ has a uniform charge density $\rho$,the electric field at a distance $r$ from the center of the sphere $(r < R)$ will be:

The electric field at a distance $\frac{3R}{2}$ from the centre of a charged conducting spherical shell of radius $R$ is $E.$ The electric field at a distance $\frac{R}{2}$ from the centre of the sphere is

$A$ 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