An electric point charge $10^{-3}\,\mu C$ is placed at the origin $(0, 0)$ of $X-Y$ co- ordinate 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.....$volt$

Three identical uncharged metal spheres are at the vertices of an equilateral triangle. One at a time, a small sphere is connected by a conducting wire with a large metal sphere that is charged. The center of the large sphere is in the straight line perpendicular to the plane of equilateral triangle and passing through its centre (see figure). As a result, the first small sphere acquires charge $q_1$ and second charge $q_2 (q_2 < q_1)$ . The charge that the third sphere $q_3$ will acquire is (Assume $l >> R$ , $l >> r$ , $d >> R$ , $d >> r$ )

Two similar tiny balls of mass $m$, each carrying charge $q$ are hung from silk thread of  length $l$ as shown in Fig. These are separated by a distance $x$ and angle $2 \theta \sim 10$. Then for equilibrium :-

The equivalent capacitance between points $A$ and $B$ of the circuit shown will be

A point charge $q$ is situated at a distance $d$ from one end of a thin non - conducting rod of length $L$ having a charge $Q$ (uniformly distributed along its length) as shown in fig.Then the magnitude of electric force between them is

Electric field at a place is $\overrightarrow E  = {E_0}\widehat i\,\,V/m$. A particle of charge $+q_0$ moves from point $A$  to $B$ along a circular path find work done in this motion by electric field :-