Question

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 $x y$-plane with its center at $(b, 0)$. All lengths are measured in meters.

The value of $b$ is _______ meter.

Answer 1

$b = a +$ radius
$=\frac{2 \sqrt{3}}{\sqrt{3}+1}+\sqrt{3}=\frac{2 \sqrt{3}+3+\sqrt{3}}{1+\sqrt{3}}$
$=\frac{3 \sqrt{3}+3}{1+\sqrt{3}}=3$
Center $=(3,0)$