Energy Density in the Electric Field of a Charged Sphere

[UWGGEOL]

Homework Statement

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

Homework Equations

u=1/2$$\(epsilon x E^2)<br /> E=kq/r^2<br /> <br /> <br /> <h2>The Attempt at a Solution</h2><br /> I have tried this like an example given in my book, which gives the q value, but since q=CV, can't 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?$$

 

[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.

 

[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.

 

[borgwal]

Oh, you probably just confused diameter and radius.

 

[UWGGEOL]

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