question_answer

Electric charges of \[+10\mu C,\ +5\mu C,\ -3\mu C\] and \[+8\mu C\] are placed at the corners of a square of side \[\sqrt{2}\]m. the potential at the centre of the square is [KCET (Engg./Med.) 1999]

A)            1.8 V                                        

B)            \[1.8\times {{10}^{6}}\] V

C)            \[1.8\times {{10}^{5}}\]V

D)                                      \[1.8\times {{10}^{4}}\]V

Correct Answer: C

Solution :

             Length of each side of square is  so distance of it?s centre from each corner is \[\frac{\sqrt{2}}{\sqrt{2}}=1m.\] Potential at the centre \[V=9\times {{10}^{9}}\left[ \frac{10\,\times {{10}^{-6}}}{1}+\frac{5\times {{10}^{-6}}}{1}-\frac{3\times {{10}^{-6}}}{1}+\frac{8\times {{10}^{-6}}}{1} \right]\]    \[=\text{ }1.8\times {{10}^{5}}V\]