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. Final charge distribution on the surfaces as
$-Q$ on inner surface, $-q$ on outer surface
$-Q$ on inner surface, $(-q +Q)$ on outer surface
$+Q$ on the inner surface, $(-q\,-Q)$ on the outer surface
The charge $-q$ is spread uniformly between inner and outer surface
A series combination of $n_1$ capacitors, each of value $C_1$, is charged by a source of potential difference $4V$. When another parallel combination of $n_2$ capacitors, each of value $C_2$, is charged by a source of potential difference $V$ , it has the same (total) energy stored in it, as the first combination has. The value of $C_2$ , in terms of $C_1$, is then
Two spherical conductors $A$ and $B$ of radii $1\, mm$ and $2\, mm$ are separated by a distance of $5\, cm$ and are uniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces of spheres $A$ and $B$ is-
A parallel plate capacitor with air between the plates has a capacitance of $9\ pF$ . The separation between its plates is $ 'd'$ .The space between the plates is now filled with two dielectrics. One of the dielectric has dielectric constant $K_1 = 6$ and thickness $\frac {d}{3}$ while the other one has dielectric constant $K_2 = 12$ and thickness $\frac {2d}{3}$ . Capacitance of the capacitor is now ......... $pF$
$A$ and $C$ are concentric conducting spherical shells of radius $a$ and $c$ respectively. $A$ is surrounded by a concentric dielectric radius $a$ , outer radius $b$ and dielectric constant $k$ . If sphere $A$ be given a charges $Q$ , the potential at the outer surface of the dielectric is
Consider a cube of uniform charge density $\rho$. The ratio of electrostatic potential at the centre of the cube to that at one of the corners of the cube is