Question

Point charge $q_{1}=2\, \mu C$ and $q_{2}=-1\, \mu C$ are kept at points $x=0$ and $x=6$, respectively. Electrical potential will be zero at points

• A. x = 2 and x = 9
• B. x = 1 and x = 5
• C. x = 4 and x = 12
• D. x = -2 and x = 2

Answer 1

Answer: (C)

Potential will be zero at two points.

At internal point $(M)$,
$\frac{1}{4 \pi \varepsilon_{0}} \times\left[\frac{2 \times 10^{-6}}{(6-l)}+\frac{\left(-1 \times 10^{-6}\right)}{l}\right]=0$
$\Rightarrow l=2$
So distance of $M$ from origin, $x=6-2=4$
At exterior point $(N)$,
$\frac{1}{4 \pi \varepsilon_{0}} \times\left[\frac{2 \times 10^{-6}}{\left(6+l'\right)}+\frac{\left(-1 \times 10^{-6}\right)}{l'}\right]=0$
$\Rightarrow l'=6$
So distance of $N$ from origin, $x=6 +6=12$