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

The correct option is C zero

The distance of point A from origin is $r_A=\sqrt{(\sqrt{2}-0{)}^2+(\sqrt{2}-0{)}^2}=\sqrt{4}=2$
The distance of point B from origin is $r_B=\sqrt{(2-0{)}^2+(0-0{)}^2}=\sqrt{4}=2$
Potential at A due to charge $Q={10}^{-3}\mu C$ is $V_A=\frac{Q}{4\pi {ϵ}_0{r}_A}=\frac{Q}{8\pi {ϵ}_0}$ as $r_A=2$
and potential at B is $V_B=\frac{Q}{4\pi {ϵ}_0{r}_B}=\frac{Q}{8\pi {ϵ}_0}$ as $r_B=2$
Potential difference between A and B $=V_A-V_B=\frac{Q}{8\pi {ϵ}_0}-\frac{Q}{8\pi {ϵ}_0}=0$ volt.