Two point charges $-Q$ and $+Q / \sqrt{3}$ are placed in the xy-plane at the origin $(0,0)$ and a point $(2,0)$, respectively, as shown in the figure. This results in an equipotential circle of radius $R$ and potential $V =0$ in the $xy$-plane with its center at $(b, 0)$. All lengths are measured in meters.

($1$) The value of $R$ is. . . . meter.

($2$) The value of $b$ is. . . . . .meter.

Two charge $ + \,q$ and $ - \,q$ are situated at a certain distance. At the point exactly midway between them

Electric field at a point $(x, y, z)$ is represented by $\vec E = 2x\hat i + {y^2}\hat j$ if potential at $(0,0,0)$ is $2\, volt$ find potential at $(1, 1, 1)$

Two electric charges $12\,\mu C$ and $ - 6\,\mu C$ are placed $20\, cm$ apart in air. There will be a point $P$ on the line joining these charges and outside the region between them, at which the electric potential is zero. The distance of $P$ from $ - 6\,\mu C$ charge is.......$m$

Find the potential $V$ of an electrostatic field $\vec E = a\left( {y\hat i + x\hat j} \right)$, where $a$ is a constant.

Four point charges $-Q, -q, 2q$ and $2Q$ are placed, one at each comer of the square. The relation between $Q$ and $q$ for which the potential at the centre of the square is zero is