The electric field at a distance $r$ from the centre in the space between two concentric metallic spherical shells of radii $r_1$ and $r_2$ carrying charges $Q_1$ and $Q_2$ respectively is $(r_1 < r < r_2)$.

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.

An electron revolves around an infinite cylindrical wire having a uniform linear charge density of $2 \times 10^{-8} \, C \cdot m^{-1}$ in a circular path under the influence of an attractive electrostatic field,as shown in the figure. The velocity of the electron with which it is revolving is $......... \times 10^6 \, m \cdot s^{-1}$. (Given: mass of electron $= 9 \times 10^{-31} \, kg$)

Let there be a spherically symmetric charge distribution with charge density varying as $\rho (r) = \rho _0 \left( \frac{5}{4} - \frac{r}{R} \right)$ 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 $r (r < R)$ from the origin is given by:

An infinitely long solid cylinder of radius $R$ has a uniform volume charge density $\rho$. It has a spherical cavity of radius $R/2$ with its centre on the axis of the cylinder,as shown in the figure. The magnitude of the electric field at the point $P$,which is at a distance $2R$ from the axis of the cylinder,is given by the expression $\frac{23\rho R}{16K\varepsilon_0}$. The value of $K$ is