Acapacitor is formed from two concentric spherical conducting shells separated by vacuum. the inner sphere has radius 11.0 cm , and the outer sphere has radius 16.5 cm . a potential difference of 100 v is applied to the capacitor. part a what is the energy density at r= 11.1 cm , just outside the inner sphere? part b what is the energy density at r = 16.4 cm , just inside the outer sphere? how can i solve this if i have no q!

Part A)
First of all, let's convert the radii of the inner and the outer sphere:


The capacitance of a spherical capacitor which consist of two shells with radius rA and rB is



Then, from the usual relationship between capacitance and voltage, we can find the charge Q on each sphere of the capacitor:


Now, we can find the electric field at any point r located between the two spheres, by using Gauss theorem:

from which

In part A of the problem, we want to find the electric field at r=11.1 cm=0.111 m. Substituting this number into the previous formula, we get


And so, the energy density at r=0.111 m is


Part B) The solution of this part is the same as part A), since we already know the charge of the capacitor: . We just need to calculate the electric field E at a different value of r: r=16.4 cm=0.164 m, so


And therefore, the energy density at this distance from the center is