Consider a uniform spherical volume charge distribution of radius $R$. Which of the following graphs correctly represents the magnitude of the electric field $E$ at a distance $r$ from the centre of the sphere?

Obtain the expression for the electric field due to a straight wire of infinite length with a linear charge density $\lambda$.

$A$ 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:

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

The electric field near a conducting surface having a uniform surface charge density $\sigma$ is given by:

The volume charge density in a spherical ball of radius $R$ varies with distance $r$ from the centre as $\rho(r)=\rho_0\left[1-\left(\frac{r}{R}\right)^3\right]$,where $\rho_0$ is a constant. The radius at which the electric field would be maximum is