# Energy Density in the Electric Field of a Charged Sphere

1. Oct 12, 2008

### UWGGEOL

1. The problem statement, all variables and given/known data
A charged isolated metal sphere of diameter 10cm has a potential of 8000V relative to V=0 at infinity. Calculate the energy density in the electric field near the surface of the sphere

2. Relevant equations
u=1/2[tex]\(epsilon x E^2)
E=kq/r^2

3. The attempt at a solution
I have tried this like an example given in my book, which gives the q value, but since q=CV, cant i find C of the sphere, solve for q, put that into E, and subsequently solve for u? The answer in my book is .11 J/m^3, but when i use the above strategy, I get around .028. Could someone point me in the right direction?

2. Oct 12, 2008

### borgwal

Express V in terms of q and r, then solve for q. It's a slightly roundabout way to calculate the energy density this way, but since you want to find q, this will work.

Last edited: Oct 12, 2008
3. Oct 13, 2008

### UWGGEOL

I tried that using V=kq/r and put q into E=kq/r^2. I also got E using V=Ed and got about 80000 V/m or N/C both times. I still get around .028 J/m^3 for my answer when i put that into the density formula.

4. Oct 13, 2008

### borgwal

Oh, you probably just confused diameter and radius.

5. Oct 14, 2008

### UWGGEOL

Thats exactly what i did wrong. I corrected and got .11J/m^3. thanks