Question

An electric charge ${10}^{−3}μC$ 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

• A. 9 V
• B. zero
• C. 2 V
• D. 4.5 V

Answer 1

Answer: (B)

Potential at A due to charge at O
$V_A=\frac{1}{4Ï€{Î\mu }_0}=\frac{({10}^{−3})}{OA}$
$=\frac{1}{4Ï€{Î\mu }_0}.\frac{({10}^{−3})}{\sqrt{{(\sqrt{2})}^2}+{(\sqrt{2})}^2}$
$=\frac{1}{4Ï€{Î\mu }_0}\frac{{10}^{−3}}{2}$
Potential at B due to charge at O
$V_B=\frac{1}{4Ï€{Î\mu }_0}.\frac{({10}^{−3})}{OB}$
$=\frac{1}{4Ï€{Î\mu }_0}.\frac{({10}^{−3})}{2}$
So, $V_A−V_B=0$