Question

A cube made of insulating material has uniform charge distribution throughout its volume. Taking the electric potential due to this charged cube at infinity to be zero, the potential at the center is found to be $V_o.$ The potential at one of its corners is

• A. $\frac{V_o}{8}$
• B. $\frac{V_o}{4}$
• C. $\frac{V_o}{2}$
• D. $V_o$

Answer 1

The correct option is C $\frac{V_o}{2}$

Let side of cube is $a$, this cube can be assumed to be made from 8 cubes of side $a/2$ each. If potential at corner of this cube of side $a$ is $V_o$, the potential due to each of these eight smaller cubes is $\frac{V_o}{8}$. So, the potential due to a cube of side $\frac{a}{2}$ at its corner is $\frac{V_o}{8}$.


Since $\left[V\right]=\left[\frac{kq}{d}\right]=\left[\frac{\rho l^3}{l}\right]=\left[\rho l^2\right]$
So by looking at the units, potential is proportional to $l^2$.

So if the side of the cube is changed from $\frac{a}{2}$ to $a$, the potential at the centre becomes $\frac{V_o}{8}\times 2^2=\frac{V_o}{2}$.