Question

A capacitor is formed from two concentric spherical conducting shells separated by vacuum. The inner sphere has radius 11.5 , and the outer sphere has radius 14.0 . A potential difference of 140 is applied to the capacitor.

What is the energy density at = 11.6 , just outside the inner sphere?

What is the energy density at = 13.9 , just inside the outer sphere?

Answer 1

The energy density in a spherical capacitor is given by\[1/2 \epsilon _{0}E ^{2}(r)\]
Where E(r) is the E field as a function of distance from the center to the outer shell. Since you know the voltage applied and the distance between the shells, you know the electric field, which is in V/m. Can you get it with this hint?

Answer 2

Also recognize that the formula for capacitance of two concentric shells is \[4pi \epsilon _{0}/[(1/a)-(1/b)]\] where a is the small radius and b is the big one. This will help in the formula C=Q/V

Answer 3

im sorry but im still a bit confused

Answer 4

1. work out field by Gauß's law, assuming central sphere bears +Q charge
2. integrate to get potential difference and equate to given value
3. work out desired energy density using @egenriether's formula

Answer 5

Thank you!!