An electric 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 $\left( {\sqrt 2 ,\sqrt 2 } \right)$ and $(2,0)$  respectively. The potential difference between the points $A$ and $B$ will be.......$V$

Three concentric spherical metallic shells $X , Y$ and $Z$ of radius $a , b$ and c respectively $[ a < b < c ]$ have surface charge densities $\sigma,-\sigma$ and $\sigma$, respectively. The shells $X$ and $Z$ are at same potential. If the radii of $X$ and $Y$ are $2\,cm$ and $3\,cm$, respectively.The radius of shell $Z$ is $......cm$.

There are four concentric shells $A, B, C $ and $D $ of radii $ a, 2a, 3a$  and $4a$ respectively. Shells $B$ and $D$ are given charges $+q$ and $-q$ respectively. Shell $C$ is now earthed. The potential difference $V_A - V_C $ is : 

An arc of radius $r$ carries charge. The linear density of charge is $\lambda$ and the arc subtends a angle $\frac{\pi }{3}$ at the centre. What is electric potential at the centre

Electric charges of $+10\,\mu\, C, +5\,\mu\, C, -3\,\mu\, C$ and $+8\,\mu\, C$ are placed at the corners of a square of side$\sqrt 2\,m$ . The potential at the centre of the square is

At the centre of a half ring of radius $R=10 \mathrm{~cm}$ and linear charge density $4 \mathrm{n} \mathrm{C} \mathrm{m}^{-1}$, the potential is $x \pi V$. The value of $x$ is  . . . . .