The surface charge density of a thin charged disc of radius $R$ is $\sigma$. The value of the electric field at the centre of the disc is $\frac{\sigma}{2\epsilon_0}$. With respect to the field at the centre,the electric field along the axis at a distance $R$ from the centre of the disc:

Which graph shows the variation of the electric field of a uniformly charged non-conducting sphere with respect to the distance $(r)$ from the centre?

An electrostatic field in a region is radially outward with magnitude $E = \alpha r$,where $\alpha$ is a constant and $r$ is the radial distance. The charge contained in a sphere of radius $R$ in this region (centered at the origin) 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.

$A$ spherical shell with an inner radius $a$ and an outer radius $b$ is made of conducting material. $A$ point charge $+Q$ is placed at the centre of the spherical shell and a total charge $-q$ is placed on the shell. Find the final charge distribution on the surfaces.

In the figure,the inner (shaded) region $A$ represents a sphere of radius $r_A=1$,within which the electrostatic charge density varies with the radial distance $r$ from the center as $\rho_A=k r$,where $k$ is positive. In the spherical shell $B$ of outer radius $r_B$,the electrostatic charge density varies as $\rho_B=\frac{2 k}{r}$. Assume that dimensions are taken care of. All physical quantities are in their $SI$ units. Which of the following statement$(s)$ is(are) correct?