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
$V_A=\frac{1q}{4\pi {\epsilon }_0{r}_1}$
$=\frac{1}{4\pi {\epsilon }_0}\frac{10^{-3}\times 10^{-6}}{2}$
Potential at point $B$ is
$V_B=\frac{1}{4\pi {\epsilon }_0}\frac{q}{r^2}=\frac{1}{4\pi {\epsilon }_0}\frac{10^{-3}\times 10^{-6}}{2}$
$\therefore V_A-V_B=0$