Three isolated metal spheres $A$,$B$,and $C$ have radii $R$,$2R$,and $3R$ respectively,and the same charge $Q$. If $U_A$,$U_B$,and $U_C$ are the energy densities just outside the surfaces of the spheres,then the relation between $U_A$,$U_B$,and $U_C$ is:

$A$ spherical conductor of radius $10 \, cm$ has a charge of $3.2 \times 10^{-7} \, C$ distributed uniformly. What is the magnitude of the electric field at a point $15 \, cm$ from the centre of the sphere?
$\left(\frac{1}{4 \pi \epsilon_{0}} = 9 \times 10^{9} \, Nm^{2}/C^{2}\right)$

Consider the following statements about electric field intensity and electric potential.
$A$. The electric field intensity due to a charged spherical shell is inversely proportional to the square of its distance from the center for points outside the shell.
$B$. The electric potential due to a point charge is inversely proportional to the distance between the charge and the point.

$ABC$ is an equilateral triangle. Charges $+q$ are placed at each corner. The electric intensity at $O$ will be

Equal charges $q$ are placed at the vertices $A$ and $B$ of an equilateral triangle $ABC$ of side $a$. The magnitude of the electric field at point $C$ is:

$A$ thin semi-circular ring of radius $r$ has a positive charge $q$ distributed uniformly over it. The net electric field $\vec{E}$ at the centre $O$ is