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)  4.5V                                     

B)  9V

C)  zero                                     

D)  2V

Correct Answer: C

Solution :

                 \[OA=\sqrt{{{(\sqrt{2})}^{2}}+{{(\sqrt{2})}^{2}}}\]                                 \[OA=2={{r}_{1}}\] and                        \[OB=2={{r}_{2}}\] 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)