Potential energy for magnetic fields

[jaejoon89]

Homework Statement

A circular 10 turn coil that has a radius of 0.05 m and current of 5A lies in the xy plane with a uniform magnetic field B = 0.05 T i + 0.12 T k (i and k are the unit vectors). What's the potential energy for the system?

Homework Equations

U = -m*B where m is the dipole moment = I*A

The Attempt at a Solution

B = sqrt((0.05 T)^2 + (0.12 T)^2) = 0.13 T

So for this I would get U = -0.00511 J, but the answer key says -0.000472 J... where's the mistake?

 

[jaejoon89]

I'm assuming from the answer that the magnetic moment must not be aligned with the field, but how do you know this given the problem? And how do you calculate this?

 

[Olfus]

Well, we have to keep in mind that -m*B is actually a "dot product". ;)