# Magnetic Potential Energy

by exitwound
Tags: energy, magnetic, potential
 P: 292 1. The problem statement, all variables and given/known data 2. Relevant equations $$U = -\vec \mu \cdot \vec B$$ 3. The attempt at a solution As you can see, I calculated $\mu$ = 4.08x10-3 and got the torque on the loop which is shown in the answer above. The potential energy is defined above as $$U = -\vec \mu \cdot \vec B = -\mu B\cos\theta$$ I have to find the angle between the two vectors which I can do using: $$\frac{\vec \mu \cdot \vec B}{|\mu||B|} = cos \theta$$ But what I came up with wasn't right. From the first part, $$\mu \vec n = (4.08x10^-3)(.6\hat i -.8 \hat j) = 2.45x10^-3 \hat i - 3.27x10^-3 \hat j$$ If: μx = 2.45e-3 Bx = .25 μy = -3.27e-3 By = 0 μz = 0 Bz = .3 -------------------------- $|\mu|^2 = (2.45x10^-3)^2 + (-3.27x10^-3)^2$ $|\mu| = 4.09x10^-3$ $|B|^2 = (.25)^2 + (.3)^2$ $|B| = 3.91x10^-1$ $$\vec \mu \cdot \vec B = \mu_xB_x + \mu_yB_y + \mu_zB_z$$ $$\frac{\mu_xB_x + \mu_yB_y + \mu_zB_z}{\mu B} = cos \theta$$ When I put in the numbers, I get 66.8 degrees between the two vectors. Putting this back into the $U = -\vec \mu \cdot \vec B = -\mu B\cos\theta$ equation gives the wrong answer. Where's the mistake(s)?