Question

Consider a cube of uniform charge density $\rho$. The ratio of electrostatic potential at the centre of the cube to that at one of the corners of the cube is?

• A. $2$
• B. $\sqrt{3}/2$
• C. $\sqrt{2}$
• D. $1$

Answer 1

Answer: (A)

$2$

Imagine putting together 8 such cubes to form a large cube with twice the side length, now the potential at the center of this new larger cube is 8 times the potential at the corner of each of the smaller cube if they are isolated.

The charge of the cube is also 8 times that of the original cube but the side length is only twice. That means that the potential at the center of this larger cube is 4 times that of at the center of the regular cube.

So the ratio comes out to be $\frac{8}{4}=2$

Option (A) is correct