Finding energy from dipole moment - Helmholtz pair?

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Homework Help Overview

The discussion revolves around calculating energy from the dipole moment in the context of a Helmholtz pair setup. Participants are exploring the implications of the dipole moment's interaction with a magnetic field.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to understand the energy calculation related to the dipole moment and its interaction with the magnetic field. Questions arise regarding the sign of the energy expression and the angle involved in the calculation.

Discussion Status

There is an active exploration of the relationships between the dipole moment, the magnetic field, and the energy expression. Some participants are questioning the assumptions made about the angle and the resulting energy sign, indicating a productive dialogue without a clear consensus yet.

Contextual Notes

Participants are considering the implications of the angle θ in the energy equation and the potential for negative energy values, which raises questions about the physical interpretation of the results. There is also a mention of the need for a diagram to clarify the setup.

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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?

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Your work looks very good to me. But what should be the sign of the dot product of m and B?
 
TSny said:
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?
 
Sorry, I wasn't very clear.

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

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