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