question_answer

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)  9 V             

B)  zero

C)  2 V             

D)  4.5 V

Correct Answer: B

Solution :

 Potential at A due to charge at O \[{{V}_{A}}=\frac{1}{4\pi {{\varepsilon }_{0}}}=\frac{({{10}^{-3}})}{OA}\] \[=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{({{10}^{-3}})}{\sqrt{{{(\sqrt{2})}^{2}}}+{{(\sqrt{2})}^{2}}}\] \[=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{{{10}^{-3}}}{2}\] Potential at B due to charge at O \[{{V}_{B}}=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{({{10}^{-3}})}{OB}\] \[=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{({{10}^{-3}})}{2}\] So, \[{{V}_{A}}-{{V}_{B}}=0\]