How Does Torque Relate to Magnetic Dipole Moment in Physics?

[ghoul]

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.

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.

The Attempt at a Solution

This is all I know how to do.

 

[I like Serena]

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.

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.

The Attempt at a Solution

This is all I know how to do.

Hi mister ghoul!

What is $\mathbf m$?

 

[ghoul]

i mister ghoul!

What is $\mathbf m$?

Hi,
I believe that m is magnetic dipole moment. m = Ia

 

[I like Serena]

Hi,
I believe 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.