$A$ long cylindrical volume contains a uniformly distributed charge of density $\rho \; C m^{-3}$. The electric field inside the cylindrical volume at a distance $x = \frac{2 \varepsilon_{0}}{\rho} \; m$ from its axis is $....... V m^{-1}$.

Obtain an expression for the electric field at the surface of a charged conductor.

Electric field at a point varies as $r^0$ for

$A$ sphere of radius $R$ has a uniform distribution of electric charge in its volume. At a distance $x$ from its centre,for $x < R$,the electric field is directly proportional to

$\sigma$ is the uniform surface charge density of a thin spherical shell of radius $R$. The electric field at any point on the surface of the spherical shell is:

$A$ solid sphere of radius $R$ has a charge $Q$ distributed in its volume with a charge density $\rho = \kappa r^a$,where $\kappa$ and $a$ are constants and $r$ is the distance from its centre. If the electric field at $r = \frac{R}{2}$ is $\frac{1}{8}$ times that at $r = R$,find the value of $a$.