Finding energy from dipole moment - Helmholtz pair?

In summary, the conversation discusses the sign and value of the dot product of m and B, as well as the direction of the magnetic field produced by a loop and the value of theta. The final conclusion is that the value of theta is not 90 degrees and the direction of the magnetic field must be considered in the calculations.
  • #1
smileandbehappy
66
0
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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  • #2
Your work looks very good to me. But what should be the sign of the dot product of m and B?
 
  • #3
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?
 
  • #4
Sorry, I wasn't very clear.

##U = -\vec{m} \cdot \vec{B}= -m \; B \cos \theta##. What is the value of ##\theta##?
 
  • #5
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...
 
  • #6
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?
 

1. How does a Helmholtz pair create energy from dipole moment?

A Helmholtz pair is a set of two identical magnets placed in parallel and separated by a distance equal to their radius. When a current is passed through the magnets, they create a magnetic field with opposite polarity. This results in a dipole moment, or the measure of the separation between the two poles. The interaction between the magnets' magnetic fields creates a torque, which can be used to do work and generate energy.

2. What are the applications of using Helmholtz pairs to find energy from dipole moment?

Helmholtz pairs are commonly used in electromagnetic generators and motors. They can also be used to create a stable magnetic field for particle accelerators and in scientific research for studying magnetic fields.

3. How do the dimensions and orientation of the Helmholtz pair affect the energy generated from dipole moment?

The energy generated from a Helmholtz pair is directly proportional to the square of the current passing through the magnets and the distance between the magnets. The orientation of the magnets also plays a role, as they must be aligned in parallel for the dipole moment to be created and for the torque to be generated.

4. Are there any disadvantages to using Helmholtz pairs for energy production?

One disadvantage of using Helmholtz pairs for energy production is that they require a constant current to maintain the magnetic field and generate energy. They also have a limited range of motion and can only generate energy within a certain distance between the magnets.

5. How does the energy generated from a Helmholtz pair compare to other methods of energy production?

The energy generated from a Helmholtz pair is relatively small compared to other methods of energy production, such as fossil fuels or nuclear energy. However, it is a renewable source of energy and does not produce harmful emissions. Therefore, it can be a valuable supplement to other energy sources and has potential for use in specific applications, such as small-scale power generation or in scientific research.

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