# Energy density of magnetic field in a solenoid

1. Aug 4, 2013

### mdf730

1. The problem statement, all variables and given/known data

A solenoid that is 117 cm long has a cross-sectional area of 20.0 cm2. There are 1010 turns of wire carrying a current of 9.56 A. (a) Calculate the energy density of the magnetic field inside the solenoid. (b) Find the total energy in joules stored in the magnetic field there (neglect end effects).

2. Relevant equations

B = μo*n*I, where n=N/l
energy density = B^2/(2*μo)
total energy = answer to part a times the volume

3. The attempt at a solution

Plugging the formulas into each other, I got

(((1010/1.17)*9.56*4*10^-7)^2)/(8*10^-7) = 13.6 J/m^3 for part (a) and
13.6*.2*1.17 = 3.19 for part (b)

Both are incorrect.

2. Aug 4, 2013

### BruceW

for part a, you have used μo to be 4*10^-7 but this is not the right definition. And for part b, 20cm^2 is not equal to 0.2m^2 (remember that 100cm^2 is not 1m^2). Apart from that, your working looks good.

3. Aug 4, 2013

### mdf730

Oh, thank you! I hate when I miss stupid little things like that.

4. Aug 4, 2013

### BruceW

hehe. yeah it is annoying when that happens.