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

Two concentric shells of radii $R$ and $3R$ are placed as shown in the figure. The outer shell carries a charge $Q$. The inner shell is grounded. Find the electric field at point $P$,which is at a distance $2R$ from the center.

According to Gauss's Theorem,the electric field of an infinitely long straight wire is proportional to

The line $AA^{\prime}$ lies on a charged infinite conducting plane which is perpendicular to the plane of the paper. The plane has a surface charge density $\sigma$. $B$ is a ball of mass $m$ with a like charge of magnitude $q$. $B$ is connected by a string to a point on the line $AA^{\prime}$. The tangent of the angle $\theta$ formed between the line $AA^{\prime}$ and the string is:

The net electric field at point $P$ due to the segments $dq_1$ and $dq_2$ of a uniformly charged spherical shell is ...... ($C$ is the center of the shell.)

If the uniform surface charge density on an infinite plane sheet is $\sigma$,the electric field near the surface will be . . . . . . .