Calculate the energy associated with the magnetic field of a solenoid

[figureskater]

Homework Statement

Calculate the energy associated with the magnetic field of a 191-turn solenoid in which a current of 1.37 A produces a magnetic flux of 3.52 10-4 T · m2 in each turn.
mJ

uo=4pie x10^-7

Homework Equations

ub=B^2/2uo(the constant)
U=1/2LI^2

The Attempt at a Solution

ub=(3.52x10^-4)^2/2(4piex10^-7)

I tried this and the answer i got 49.29mJ was incorrect. Not sure if I am missing something or using the incorrect formula here. Its due Tuesday March 27 by midnight thanks.

 

[clementc]

I'm not 100% sure
but I think the formula you're missing here is the one for inductance:

$$L=\frac{N\Phi_B}{i}$$

 

[Phrak]

An interesting question. How does one unambiguously measure the energy of a magnetic field that is first zero valued before the current is turned on at time t0? The field then expands at the speed of light. Wouldn't it have less energy at time t1>t0 than at time t=infinity as it fills all space?

 

[rexrino]

"...Wouldn't it have less energy at time t1>t0 than at time t=infinity as it fills all space? "

I don't believe it fills all space. I think the field is limited to the area where the field lines are able to be fully realized. When the lines are broken, the field is at the end of it's limits.

 

[Phrak]

Not in general, but but any case, the Energy of a solenoid is given by W=½I²L.