Question

A charged isolated metal sphere of diameter 12 cm has a potential of 9200 V relative to V = 0 at infinity. Calculate the energy density in the electric field near the surface of the sphere.

Answer 1

0.1 J/m³

Step-by-step explanation:

We know that

V = k Q / R

We also know that

E = k Q / R²

Joining the two equations together, we have

E = V / R

To solve the question proper, we'd be using the formula

u = 1/2 E• E², substitute for E, we have

u = 1/2 E• (V/R)²

u = 1/2 * 8.85*10^-12 * (9000 / 0.06)²

u = 1/2 * 8.85*10^-12 * 150000²

u = 1/2 * 8.85*10^-12 * 2.25*10^10

u = 1/2 * 0.199125

u = 0.0996

u = 0.1 J/m³

The energy density is 0.1 J/m³