Consider a cube having a uniform volume charge density ρ. Find the ratio of electrostatic potential at the centre of the cube to that potential at a corner of the cube.

Question

Consider a cube having a uniform volume charge density ρ. Find the ratio of electrostatic potential at the centre of the cube to that potential at a corner of the cube. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Consider a uniformly charged cube of side length

a

, and charge density

ρ

.

From dimensional analysis

V_{corner} \propto \frac{ρ a ^{3}}{a}

V_{corner} \propto ρ a^{2}

Now consider a big cube of side length

2 a

\frac{V _{comer}^{Big}}{V _{comer}^{small}} = (\frac{2 a}{a})^{2} = \frac{4}{1}

....(i)
But it is clear from the figure that

V_{centre}^{Big} = 8 V_{Comer}^{small}

∴

From (i)

\frac{V _{Comer}^{Big}}{\frac{1}{8} V _{Centre}^{Big}} = \frac{4}{1}

\Rightarrow \frac{V _{Comer}}{V _{centre}} = \frac{1}{2}

Q. Consider a cube having a uniform volume charge density ρ. Find the ratio of electrostatic potential at the centre of the cube to that potential at a corner of the cube.

Q. Consider a cube having a uniform volume charge density $ρ$ . Find the ratio of electrostatic potential at the centre of the cube to that potential at a corner of the cube.