Question

A point charge $q_1=+2\mu C$ is placed at the origin of the $XY$ coordinate system. A second charge $q_2=-3\mu C$ is placed on the $y-$axis at $y=100cm$. At what points on the $y-$axis is the electric potential zero?

• A. $y=-200cm$
• B. $y=200cm$
• C. $y=40cm$
• D. None of the above

Answer 1

Answer: (A), (C)

$y=-200cm$
$y=40cm$

Let $P_1$ and $P_2$ be the points where electric potential is zero.

At point $P_1$ :

$V_{P_1}=\frac{k{q}_1}{y_1}+\frac{k{q}_2}{(100-y_1)}=0$

$\therefore$ $\frac{2}{y_1}+\frac{(-3)}{(100-y_1)}=0$

OR $\frac{2}{y_1}=\frac{3}{(100-y_1)}$

$⟹$ $y_1=40$ $cm$

At point $P_2$ :

$V_{P_2}=\frac{k{q}_1}{y_2}+\frac{k{q}_2}{(y_2+100)}=0$

$\therefore$ $\frac{2}{y_2}+\frac{(-3)}{(100+y_2)}=0$

OR $\frac{2}{y_2}=\frac{3}{(100+y_2)}$

$⟹$ $y_2=-200$ $cm$

Thus electric potential is zero at $y=40cm$ and $y=-200cm$.