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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 between the points $A$ and $B$ will be......$V$
$9$
$0$
$2$
$4.5$
Solution
The distance of point $A(\sqrt{2}, \sqrt{2})$ from the origin,
$O A=|\overrightarrow{r_{1}}|=\sqrt{(\sqrt{2})^{2}+(\sqrt{2})^{2}}=\sqrt{4}=2$units
The distance of point $\mathrm{B}(2,0)$ from the origin,
$O B=|\overrightarrow{r_{2}}|=\sqrt{(2)^{2}+(0)^{2}}=2$ units
Now, potential at $\mathrm{A}, V_{A}=\frac{1}{4 \pi \in 0} \cdot \frac{Q}{(O A)}$
Potential at $\mathrm{B}, V_{B}=\frac{1}{4 \pi \in 0} \cdot \frac{O}{(O B)}$
$\therefore$ Potential difference between the points $\mathrm{A}$ and $\mathrm{B}$ is zero.
