Find the force experienced by the semicircular rod charged with a charge $q$, placed as shown in figure. Radius of the wire is $R$ and the line of charge with linear charge density $\lambda $ is passing through its centre and perpendicular to the plane of wire.
$\frac{{\lambda q}}{{2{\pi ^2}{\varepsilon _0}R}}$
$\frac{{\lambda q}}{{{\pi ^2}{\varepsilon _0}R}}$
$\frac{{\lambda q}}{{4{\pi ^2}{\varepsilon _0}R}}$
$\frac{{\lambda q}}{{4\pi {\varepsilon _0}R}}$
A positive charge $q$ is placed in a spherical cavity made in a positively charged sphere. The centres of sphere and cavity are displaced by a small distance $\vec l $ . Force on charge $q$ is :
Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius $R$, with distance $r$ from the centre $O$ is represented by:
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
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
An electrostatic field in a region is radially outward with magnitude $E$ = $\alpha r$ , where $\alpha $ is a constant and $r$ is radial distance. The charge contained in a sphere of radius $R$ in this region (centred at the origin) is