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