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Proving that torque is m X B

1. Homework Statement
Starting from the Lorentz force law, in the form of Fmag = ∫ I (d× B), show that the torque on any steady current distribution (not just a square loop) in a uniform field B is m × B.

2. Homework Equations
I looked at the solution I found in this thread here, but I don't understand the step after you take the derivative of both sides of the torque equation. Why would you use that method in the next step, and how? Where did it come from?

I have Griffiths 4ed.

3. The Attempt at a Solution
This is all I know how to do.
ubsqgCZ.jpg
 

I like Serena

Homework Helper
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1. Homework Statement
Starting from the Lorentz force law, in the form of Fmag = ∫ I (d× B), show that the torque on any steady current distribution (not just a square loop) in a uniform field B is m × B.

2. Homework Equations
I looked at the solution I found in this thread here, but I don't understand the step after you take the derivative of both sides of the torque equation. Why would you use that method in the next step, and how? Where did it come from?

I have Griffiths 4ed.

3. The Attempt at a Solution
This is all I know how to do.
ubsqgCZ.jpg
Hi mister ghoul! :oldsmile:

What is ##\mathbf m##?
 
Last edited:
i mister ghoul! :oldsmile:

What is ##\mathbf m##?
Hi,
I belive that m is magnetic dipole moment. m = Ia
 

I like Serena

Homework Helper
6,553
176
Hi,
I belive that m is magnetic dipole moment. m = Ia
Okay... so what is ##\mathbf a##?
We'll need some expression to substitute, which will hopefully lead to the requested result.
 

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