$A$ thin spherical shell of radius $R$ has charge $Q$ spread uniformly over its surface. Which of the following graphs most closely represents the electric field $E(r)$ produced by the shell in the range $0 \le r < \infty$,where $r$ is the distance from the centre of the shell?

$A$ hollow charged conductor has a tiny hole cut into its surface. Show that the electric field in the hole is $(\sigma / 2 \varepsilon_{0}) \hat{n}$,where $\hat{n}$ is the unit vector in the outward normal direction,and $\sigma$ is the surface charge density near the hole.

The magnitude of electric field on the surface of a uniformly charged metallic spherical shell is $E$. If a hole is made in it using an insulating device,then the magnitude of electric field in the hole will be

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 $r$ of the circular path from the wire is:

The electric field in a region is radially outward and at a point is given by $E = 250 r \, V/m$ (where $r$ is the distance of the point from the origin). Calculate the charge contained in a sphere of radius $20 \, cm$ centered at the origin in Coulombs $(C)$.

If two infinite plane sheets having same surface charge density $\sigma$ are placed parallel to each other,then the electric field between the two sheets is . . . . . . .