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, \[{{V}_{A}}-{{V}_{B}}=0\]