Electrostatics Question 371
Question: Four identical charges $ +50\mu C $ each are placed, one at each corner of a square of side $ 2m $ . How much external energy is required to bring another charge of $ +50\mu C $ from infinity to the centre of the square $ ( \text{Given}\frac{\text{1}}{\text{4}\pi {\varepsilon _{\text{0}}}}=9\times 10^{9}\frac{Nm^{2}}{C^{2}} ) $
Options:
A) $ 64J $
B) $ 41J $
C) $ 16J $
D) $ 10J $
Show Answer
Answer:
Correct Answer: A
Solution:
Potential at the centre of square $ V=4\times ( \frac{9\times 10^{9}\times 50\times {{10}^{-6}}}{2/\sqrt{2}} )=90\sqrt{2}\times 10^{4}V $
Work done in bringing a charge (q = 50 mC) from ¥ to centre (O) of the square is
$ W=q(V _{0}-{V _{\infty }})=qV _{0} $
therefore $ W=50\times {{10}^{-6}}\times 90\sqrt{2}\times 10^{4}=64J $
