Finding energy from dipole moment - Helmholtz pair?

[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?

 

[TSny]

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

 

[smileandbehappy]

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

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?

 

[TSny]

Sorry, I wasn't very clear.

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

 

[smileandbehappy]

Sorry, I wasn't very clear.

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

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

 

[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?