A point charge of magnitude $+ 1\,\mu C$ is fixed at $(0, 0, 0) $. An isolated uncharged spherical conductor, is fixed with its center at $(4, 0, 0).$ The potential and the induced electric field at the centre of the sphere is

Two metal spheres $A$ and $B$ of radii $a$ and $b(a < b)$ respectively are at a large distance apart. Each sphere carries a charge of $100 \mu C$. The spheres are connected by a conducting wire, then

An electric charge $10^{-3}\ \mu C$ is placed at the origin $(0, 0)$ of $X-Y$ coordinate  system. Two points $A$ and $B$ are situated at $(\sqrt 2 ,\sqrt 2 )$ and $(2, 0)$ respectively. The potential difference between the points $A$ and $B$ will be……$V$

Two metal spheres of radii ${R_1}$ and ${R_2}$ are charged to the same potential. The ratio of charges on the spheres is

Two equal positive point charges are kept at points $A$ and $B$ . The electric potential, while moving from $A$ to $B$ along straight line