Capacitor with radius finding the energy density

[sonrie]

A capacitor is formed from two concentric spherical conducting shells separated by vacuum. The inner sphere has radius 12.5 cm , and the outer sphere has radius 16.5 cm . A potential difference of 100 V is applied to the capacitor.



What is the energy density at r = 12.6 cm , just outside the inner sphere?

What is the energy density at r = 16.4 cm , just inside the outer sphere?

Equations:
U= 1/2 CV^2/Ad
U= 1/2 Eo E^2
C= EoA/d
V= Ed

C= 8.85*10^-12 *pi * .126^2/.04 =1.11*10^-11
so next i solved for U, U= .5 *1.11*10^-11 *100^2/pi*.126^2*.04=2.78*10^-5 which is not correct, Help PLease!

 

[Astronuc]

Make sure you have the correct formula for the spherical capacitor.

http://hyperphysics.phy-astr.gsu.edu/Hbase/electric/capsph.html

http://hyperphysics.phy-astr.gsu.edu/Hbase/electric/capeng.html#c2

Also, please show units when working on a problem.

 

[alphysicist]

Hi sonrie,

I believe you are using a wrong formula here. The expression

$$C=\epsilon_0 \frac{A}{d}$$

applies to a parallel plate capacitor. The spherical capacitor has a different formula.

The formula energy density = (1/2) CV^2/(Ad) is also normally used for the constant field of a parallel plate capacitor. The other one (energy density = (1/2) $\epsilon_0$ E^2) applies to any capacitor problem.

(You might also find that the formula C=Q/V is helpful.)

 

[sonrie]

Thanks!

 

[wcelectric]

How do I find E, which I need to find the energy density? Then what do I do?