#### An electric charge   is placed at the origin (0,0)of  X-Y co-ordinate system . Two points A and B are situated at respectively. The potential difference between the point  A and B will be Option 1) 4.5 volt Option 2) 9 volt Option 3) zero Option 4) 2 volt

As we learnt in

Potential Difference -

-

$\vec{r_{1}}= \sqrt{2}\hat{i}+\sqrt{2}\hat{j}$

$\left | \vec{r_{1}} \right |= r_{1}= \sqrt{\left ( \sqrt{2} \right )^{2}+\left ( \sqrt{2} \right )^{2}}= 2$

$\vec{r_{2}}= 2\hat{i}+0\hat{j}$

$or \left | \vec{r_{1}} \right |= r_{2}= 2$

$Potential \: at\: point\: A\: is\:$

$V_{A}= \frac{1q}{4\pi \varepsilon _{0}r_{1}}$

$= \frac{1}{4\pi \varepsilon _{0}}\frac{10^{-3}\times 10^{-6}}{2}$

$Potential\: at\: point\: B \: is \:$

$V_{B}=\frac{1}{4\pi \varepsilon _{0}}\frac{q}{r^{2}}= \frac{1}{4\pi \varepsilon _{0}}\frac{10^{-3}\times10^{-6} }{2}$

$\therefore V_{A}-V_{B}$ = Zero

Option 1)

4.5 volt

Incorrect

Option 2)

9 volt

Incorrect

Option 3)

zero

Correct

Option 4)

2 volt

Incorrect