The electric field at a distance of $20 \ cm$ from the center of a uniformly charged dielectric sphere of radius $R = 10 \ cm$ is $100 \ V/m$. What will be the electric field $E$ at a distance of $3 \ cm$ from the center of the sphere (in $V/m$)?

$A$ spherical shell with an inner radius $a$ and an outer radius $b$ is made of conducting material. $A$ point charge $+Q$ is placed at the centre of the spherical shell and a total charge $-q$ is placed on the shell. Find the final charge distribution on the surfaces.

$A$ cube is placed inside an electric field,$\overrightarrow{E} = 150 y^2 \hat{j}$. The side of the cube is $0.5 \, m$ and it is placed in the field as shown in the figure. The charge inside the cube is $..... \times 10^{-11} \, C$.

$A$ spherically symmetric charge distribution is characterised by a charge density having the following variations:
$\rho (r) = \rho_0 \left( 1 - \frac{r}{R} \right)$ for $r < R$
$\rho (r) = 0$ for $r \ge R$
Where $r$ is the distance from the centre of the charge distribution and $\rho_0$ is a constant. The electric field at an internal point $(r < R)$ is:

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 $\frac{23 \rho R}{16 k \varepsilon_0}$. The value of $k$ is

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