Question

A uniformly charged sphere has a potential on its surface of 450 V. At a radial distance of 8.1 m from this surface, the potential is 150 V. What is the radius of the sphere

Answer 1

The radius of the sphere is 4.05 m

Step-by-step explanation:

Given;

potential at surface,
`V_s` = 450 V

potential at radial distance,
`V_r` = 150

radial distance, l = 8.1 m

Apply Coulomb's law of electrostatic force;

`V = (KQ)/(r) \\\\V_s = (KQ)/(r) \\\\V_r = (KQ)/(r+ l)`

`450 = (KQ)/(r) ------equation (i)\\\\150 = (KQ)/(r+8.1) ------equation (ii)\\\\divide \ equation (i)\ by \ equation \ (ii)\\\\(450)/(150) = ((KQ)/(r) )*((r+8.1)/(KQ) )\\\\3 = (r+8.1)/(r) \\\\3r = r + 8.1\\\\2r = 8.1\\\\r = (8.1)/(2) \\\\r = 4.05 \ m`

Therefore, the radius of the sphere is 4.05 m