A uniform rod $AB$ of mass $m$ and length $l$ is hinged at its mid point $C$ . 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 unirorm 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 in the plane of the paper and released. The time period of small angular oscillations is

The electric field due to a uniformly charged sphere of radius $R$ as a function of the distance $r$ from its centre is represented graphically by

If an insulated non-conducting sphere of radius $R$ has charge density $\rho $. The electric field at a distance $r$ from the centre of sphere $(r < R)$ will be

Two infinitely long parallel wires having linear charge densities ${\lambda _1}$ and ${\lambda _2}$ respectively are placed at a distance of $R$ metres. The force per unit length on either wire will be $\left( {K = \frac{1}{{4\pi {\varepsilon _0}}}} \right)$

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 $\rho _0$ is a constant. The electric field at an internal point $(r < R)$ is

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