Question

An electric charge $10^{-3}\, \mu C$ is placed at the origin $(0, 0)$ of $X$ - $Y$ co-ordinate system. Two points $A$ and $B$ are situated at $(\sqrt{2}, \sqrt{2})$ and $(2, 0)$ respectively. The potential difference between the points $A$ and $B$ will be

• A. $4.5$ volt
• B. $9$ volt
• C. zero
• D. $2$ volt

Answer 1

Answer: (C)

$\vec{r}_{1} = \sqrt{2}\hat{i}+\sqrt{2}\hat{j} $
$ \left|\vec{r}_{1}\right| = r_{1} = \sqrt{\left(\sqrt{2}\right)^{2}+\left(\sqrt{2}\right)^{2}} =2 $
$ \vec{r}_{2} = 2\hat{i} +0\hat{j} $
or $\left|\vec{r}_{2}\right| = r_{2} = 2 $
Potential at point $A$ is
$V_{A} = \frac{1q}{4\pi\varepsilon_{0}r_{1}}$
$ = \frac{1}{4\pi\varepsilon_{0}} \frac{10^{-3}\times10^{-6}}{2}$
Potential at point $B$ is
$ V_{B} = \frac{1}{4\pi\varepsilon_{0}} \frac{q}{r^{2}} = \frac{1}{4\pi\varepsilon_{0}} \frac{10^{-3}\times10^{-6}}{2}$
$ \therefore V_{A} -V_{B} = 0$