Electrostatics Question 452
Question: If identical charges $ (-q) $ are placed at each corner of a cube of side b, then electric potential energy of charge $ (+q) $ which is placed at centre of the cube will be [CBSE PMT 2002]
Options:
A) $ \frac{8\sqrt{2}q^{2}}{4\pi {\varepsilon _{0}}b} $
B) $ \frac{-8\sqrt{2}q^{2}}{\pi {\varepsilon _{0}}b} $
C) $ \frac{-4\sqrt{2}q^{2}}{\pi {\varepsilon _{0}}b} $
D) $ \frac{-4q^{2}}{\sqrt{3}\pi {\varepsilon _{0}}b} $
Show Answer
Answer:
Correct Answer: D
Solution:
Length of the diagonal of a cube having each side b is $ \sqrt{3}b. $
So distance of centre of cube from each vertex is $ \frac{\sqrt{3}b}{2}. $
Hence potential energy of the given system of charge is $ U=8\times { \frac{1}{4\pi {\varepsilon _{0}}}.\frac{(-q)(q)}{\sqrt{3}b/2} }=\frac{-4q^{2}}{\sqrt{3}\pi {\varepsilon _{0}}b} $
