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

$A$ 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:

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

Consider a uniform spherical charge distribution of radius $R_1$ centred at the origin $O$. In this distribution,a spherical cavity of radius $R_2$,centred at $P$ with distance $OP = a = R_1 - R_2$ (see figure) is made. If the electric field inside the cavity at position $\vec{r}$ is $\vec{E}(\vec{r})$,then the correct statement$(s)$ is(are):

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

$A$ thin disc of radius $b = 2a$ has a concentric hole of radius $a$ in it (see figure). It carries uniform surface charge $\sigma$. If the electric field on its axis at height $h$ $(h << a)$ from its centre is given as $Ch$,then the value of $C$ is: