# How to find energy stored between two spheres?

## Homework Statement

A spherical conductor of radius 7.00 mm carries a surface charge density of 9.00 μC/mm2. A second hollow, concentric, spherical conductor has an inner radius of 7.09 mm. How much stored energy is there between the spheres?

## Homework Equations

C=Q/V
A=4pi(r^2)
C=4(pi)(Epsilon_0)((R_a*R_b)/(R_a-R_b))
surface charge density = Q/A
U=.5*Q^2/C=.5*C*V^2=.5QV

## The Attempt at a Solution

I keep getting 2.5o4e^-4 kJ but it isnt one of the answer choices. There is a 250 kJ, but that makes me off by a factor of 1 million...
A) 16kJ B) 1000kJ C) 6.4kJ D) 250kJ
Thank you very much!

Spinnor
Gold Member
Your charge density is in charge/mm^2 and the dimensions of the sphere are in mm. Do you have Epsilon_0 in the right units or did you convert mm above to m?

Yes, I did convert everything to standard units.
R_a=.00709m
R_b=.007m
σ=.009 coulombs/m^2

C=Q/V_ba=4(pi)(Epsilon_0)((R_a*R_b)/R_a-R_b))=6.1327e-11F

Surface area of inner sphere =4(pi)(.007^2)=6.1575e-4m2
σ=Q/A so Q=5.5418e-6

U=.5(Q^2/C)=.5((5.5418e-6)^2)/6.1327e-11)=2.504e-4 kJ
in kJ because that's what the answer choices are in.