Finding energy from dipole moment - Helmholtz pair?

1. May 14, 2015

smileandbehappy

Firstly apologies for not typing this out - but I need the diagram. And I have no idea where to start. I 'think' most of it is correct. BUT - I have no idea what to do with the last part of c. I thought I could just double the energy. But I'm going to get a negative energy for the system... Clearly that isn't right. I have also considered that the energies just cancel each other out... But that doesn't seem to make sense either. Any ideas?

2. May 14, 2015

TSny

Your work looks very good to me. But what should be the sign of the dot product of m and B?

3. May 14, 2015

smileandbehappy

The sign shoud be: U = -B.m

So I still get a minus sign... Or am I missing something obvious? Should I just double the U and make it positive to get the answer?

4. May 14, 2015

TSny

Sorry, I wasn't very clear.

$U = -\vec{m} \cdot \vec{B}= -m \; B \cos \theta$. What is the value of $\theta$?

5. May 14, 2015

smileandbehappy

I though ti was 90 degrees. But I am guessing I am wrong...

6. May 14, 2015

TSny

Note that $\cos 90^o = 0$, so that's not what you would like to have.

Consider the loop on the left. What is the direction of $\vec{m}$ for that loop? What is the direction of the magnetic field $\vec{B}$ produced by the loop on the right at the location of the loop on the left?