Question

Find out the points on the line joining two charges $+q$ and $3q$ (kept at a distance of $1.0m$ in that order), where electric potential is zero.

• A. $0.5m$ to the left of $q$
• B. $0.5m$ to the right of $q$
• C. $0.25m$ to the right of $q$
• D. $0.75m$ to the right of $q$

Answer 1

Answer: (A), (C)

The correct options are
A $0.5m$ to the left of $q$
C $0.25m$ to the right of $q$

Two charges $=+q$ and $3q$

distance $=1.0m$

where electric potential $=0$

$\therefore$ $\frac{Kq}{x^2}=\frac{K\times 3q}{{(R+x)}^2}$

or, $\frac{1}{x^2}=\frac{3}{R^2+2Rx+x^2}$

or, $R^2+2Rx+x^2=3x^2$

or, ${2x}^2-2Rx-R^2=0$

or, Using sridhar archarrya's law

$x=\frac{R}{2}$

$=\frac{1}{2}=0.5m$

to left of the $q$.