An infinite line charge produces a field of $9 \times 10^4 \ NC^{-1}$ at a distance of $2 \ cm$. Its linear charge density is

Consider a sphere of radius $R$ with charge density distributed as:
$\rho(r) = kr$ for $r \leq R$
$\rho(r) = 0$ for $r > R$
$(a)$ Find the electric field at all points $r$.
$(b)$ Suppose the total charge on the sphere is $2e$ where $e$ is the elementary charge. Where can two protons be embedded such that the force on each of them is zero? Assume that the introduction of the protons does not alter the charge distribution.

The charge density of a uniformly charged infinite plane is $\sigma$. $A$ simple pendulum is suspended vertically downward near it. $A$ charge $q_0$ is placed on the metallic bob. If the angle made by the string with the vertical direction is $\theta$,then . . . . . . .

Consider a solid insulating sphere of radius $R$ with charge density varying as $\rho = \rho_0 r^2$,where $\rho_0$ is a constant and $r$ is measured from the centre. Consider two points $A$ and $B$ at distances $x$ and $y$ respectively $(x < R, y > R)$ from the centre. If the magnitudes of the electric fields at points $A$ and $B$ are equal,then:

Three infinitely long charge sheets are placed as shown in the figure. The electric field at point $P$ is

The electric field at a distance $R$ from the surface of a uniformly charged nonconducting sphere of radius $R$ is $20 \,V/m$. The electric field at a distance $\frac{R}{2}$ from the centre of the sphere is $.... \,V/m$.