Calculate Energy Density of Spherical Capacitor

[AGGENGR]

A capacitor is formed from two concentric spherical conducting shells separated by vacuum. The inner sphere has radius 10.5cm , and the outer sphere has radius 15.5cm . A potential difference of 110V is applied to the capacitor.

What is the energy density at r= 10.6cm , just outside the inner sphere?

What is the energy density at r = 15.4cm , just inside the outer sphere?

u = 1/2eoE^2 & E=V/dBasically i found E-field between the shells by using E=V/d where d was the difference in radii. Then subbed that into the Energy density one. Wrong

I also tried to add radii then divide by 2 and use the given 10.6 cm value. Wrong and Wrong.

 

[gneill]

The E field won't be uniform with distance between the spheres. Recall that the field inside a charged conducting sphere due to a charge on that sphere is zero, implying that any charge on the outer sphere is not going to influence the field due to the charge on the inner sphere. So the field pattern between the spheres will look like that of a point charge, radiating outward. So the trick will be relating the field strength at a given location to the potential placed between the spheres.

Take a look at the Hyperphysics webpage on the Spherical Capacitor.