Which of the following graphs shows the variation of electric field $E$ due to a hollow spherical conductor of radius $R$ as a function of distance $r$ from the centre of the sphere

A non-conducting solid sphere of radius $R$ is uniformly charged. The magnitude of the electric field due to the sphere at a distance $r$ from its centre

Charges $Q, 2Q$ and $4Q$ are uniformly distributed in three dielectric solid spheres $1,2$ and $3$ of radii $R/2, R$ and $2 R$ respectively, as shown in figure. If magnitudes of the electric fields at point $P$ at a distance $R$ from the centre of spheres $1,2$ and $3$ are $E_1 E_2$ and $E_3$ respectively, then

Obtain the expression of electric field at any point by continuous distribution of charge on a  $(i)$ line $(ii)$ surface $(iii)$ volume.

Consider a sphere of radius $\mathrm{R}$ which carries a uniform charge density $\rho .$ If a sphere of radius $\frac{\mathrm{R}}{2}$ is carved out of it, as shown, the ratio $\frac{\left|\overrightarrow{\mathrm{E}}_{\mathrm{A}}\right|}{\left|\overrightarrow{\mathrm{E}}_{\mathrm{B}}\right|}$ of magnitude of electric field $\overrightarrow{\mathrm{E}}_{\mathrm{A}}$ and $\overrightarrow{\mathrm{E}}_{\mathrm{B}}$ respectively, at points $\mathrm{A}$ and $\mathrm{B}$ due to the remaining portion is

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