Question

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

Answer 1

Answer: 0

The position vector of $A,{\vec{r}}_1=\sqrt{2}\hat{i}+\sqrt{2}\hat{j}$
$|{\vec{r}}_1|=r_1=\sqrt{(\sqrt{2}{)}^2+(\sqrt{2}{)}^2}=2$

The position vector of $B,{\vec{r}}_2=2\hat{i}+0\hat{j}$
or $|{\vec{r}}_2|=r_2=2$
Potential at point $A$ is:
$V_A=\frac{1}{4\pi {\epsilon }_0}\frac{q}{r_1}=\frac{1}{4\pi {\epsilon }_0}\frac{10^{-3}\times 10^{-6}}{2}$
Potential at point $B$ is:
$V_B=\frac{1}{4\pi {\epsilon }_0}\frac{q}{r_2}=\frac{1}{4\pi {\epsilon }_0}\frac{10^{-3}\times 10^{-6}}{2}$