Question

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

• A. 4.5V
• B. 9V
• C. zero
• D. 2V

Answer 1

The Correct Option is C

The correct answer is C:Zero
First we have to find out the distance of point A and B from origin;
For point A: \(O A=\sqrt{(\sqrt{2})^{2}+(\sqrt{2})^{2}}\)
\(O A=2=r_{1}\) 
and for point B: \(O B=2=r_{2}\) 
The potential difference between the point \(A\) and \(B\) will be 
\(V_{A}-V_{B}=\frac{q}{4 \pi \varepsilon_{0} r_{1}}-\frac{q}{4 \pi \varepsilon_{0} r_{2}}\)
\(V_{A}-V_{B}=0\) (zero)