$A$ solid ball of radius $R$ has a charge density $\rho$ given by $\rho = \rho_0 \left( 1 - \frac{r}{R} \right)$ for $0 \leq r \leq R$. The electric field outside the ball is

If the uniform surface charge density on an infinite plane sheet is $\sigma$,the electric field near the surface will be . . . . . . .

The electric field in a certain region is acting radially outward and is given by $E = Ar$. $A$ charge contained in a sphere of radius $a$ centered at the origin of the field will be given by:

An electron is projected towards a metal plate with a surface charge density $\sigma = -2 \times 10^{-6} \ C/m^2$. If the electron strikes the plate with zero velocity,calculate the distance $d$ between the electron gun and the plate in terms of its initial kinetic energy $E_k$.

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:

$A$ uniform rod $AB$ of mass $m$ and length $l$ is hinged at its midpoint $C$. The left half $(AC)$ of the rod has linear charge density $-\lambda$ and the right half $(CB)$ has $+\lambda$,where $\lambda$ is constant. $A$ large non-conducting sheet of uniform surface charge density $\sigma$ is also present near the rod. Initially,the rod is kept perpendicular to the sheet. The end $A$ of the rod is initially at a distance $d$. Now,the rod is rotated by a small angle $\theta$ in the plane of the paper and released. The time period of small angular oscillations is: