question_answer

A cube of side b has a charge q at each of its virtues. The electric potential at the centre of the cube is:

A)  \[\frac{4q}{\sqrt{3\pi }{{\varepsilon }_{0}}b}\]        

B)  \[\frac{\sqrt{3}q}{\pi {{\varepsilon }_{0}}b}\]

C)  \[\frac{2q}{\pi {{\varepsilon }_{0}}b}\]                  

D)  zero

Correct Answer: A

Solution :

\[\therefore \]  \[Vneta{{t}_{0}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{q}{\left( \frac{b/\sqrt{3}}{2} \right)}\times 8=\frac{4q}{\sqrt{3}\pi {{\varepsilon }_{0}}b}\] (As distance of charge from the corners is \[\frac{b\sqrt{3}}{2}\])