Question

21. R Identical +1.8 C charges are fixed to adjacent corners of a square. What charge (magnitude and algebraic sign) should be fixed to one of the empty corners, so that the total electric potential at the remaining empty corner is 0 V?

Answer 1

Electric potential due to a point charge $q$ at a distance $r$ is $V=\frac{q}{4\pi \epsilon_0 r}$

Here let the charge at third corner be $Q$.

Potential at the fourth corner will be $V=\frac{1}{4\pi\epsilon_0}\left(\frac{q}{a}+\frac{q}{a\sqrt{2}}+\frac{Q}{a} \right )$

$V=\frac{1}{4\pi\epsilon_0}\left(\frac{q}{a}+\frac{q}{a\sqrt{2}}+\frac{Q}{a} \right )=0$

$q+\frac{q}{\sqrt{2}}+Q=0$

$Q=-q\left(1+\frac{1}{\sqrt{2}} \right )=-1.8*10^{-6}\left(1+\frac{1}{\sqrt{2}} \right )=-3.073*10^{-6}=-3.073\,\mu C$