Two metal spheres, one of radus $R$ and the other of radius $2 R$ respectively have the same surface charge density $\sigma$. They are brought in contact and separated. What will be the new surface charge densities on them?
$\sigma_{1}=\frac{5}{6} \sigma, \sigma_{2}=\frac{5}{2} \sigma$
$\sigma_{1}=\frac{5}{2} \sigma, \sigma_{2}=\frac{5}{6} \sigma$
$\sigma_{1}=\frac{5}{2} \sigma, \sigma_{2}=\frac{5}{3} \sigma$
$\sigma_{1}=\frac{5}{3} \sigma, \sigma_{2}=\frac{5}{6} \sigma$
Aspherical 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.
Charge $- q $ is distributed on the surfaces as
A charge $q$ is distributed uniformly on the surface of a sphere of radius $R$. It is covered by a concentric hollow conducting sphere of radius $2 R$. Charge on the outer suiface of the hollow sphere will be, if it is earthed
A solid uncharged conducting sphere has radius $3a$ contains a hollowed spherical region of radius $2a$. A point charge $+Q$ is placed at a position a distance a from the common center of the spheres. What is the magnitude of the electric field at the position $r = 4a$ from the center of the spheres as marked in the figure by $P?$ $\left( {k = \frac{1}{{4\pi { \in _0}}}} \right)$
The vehicles carrying inflammable fluids usually have metallic chains touching the ground:
$64$ small drops of mercury, each of radius $ r$ and charge $q$ coalesce to form a big drop. The ratio of the surface density of charge of each small drop with that of the big drop is