Consider three concentric metallic spheres $A, B$ and $C$ of radii $a , b, c$, respectively where $a < b < c$. $A$ and $B$ are connected, whereas $C$ is grounded. The potential of the middle sphere $B$ is raised to $V$, then the charge on the sphere $C$ is

Ten charges are placed on the circumference of a circle of radius $R$ with constant angular separation between successive charges. Alternate charges $1,3,5,7,9$ have charge $(+q)$ each, while $2,4,6,8,10$ have charge $(-q)$ each. The potential $V$ and the electric field $E$ at the centre of the circle are respectively

(Take $V =0$ at infinity $)$

A uniform electric field of $20\, N/C$ exists along the $x$ -axis in a space. The potential  difference $(V_B -V_A)$ for the point $A(4\,m, 2\,m)$ and $B(6\,m, 5\,m)$ is.....$V$

The charge given to a hollow sphere of radius $10\, cm$ is $3.2×10^{-19}\, coulomb$. At a distance of $4\, cm$ from its centre, the electric potential will be

A charge $Q$ is distributed over three concentric spherical shell of radii $a, b, c (a < b < c)$ such that their surface charge densities are equal to one another. The total potential at a point at distance $r$ from their common centre, where $r < a$, would be

A conducting sphere of radius $R$ is given a charge $Q$. The electric potential and the electric field at the centre of the sphere respectively are