Proving that torque is m X B

In summary, the conversation discusses using the Lorentz force law to show that the torque on any steady current distribution in a uniform magnetic field can be expressed as m × B, where m is the magnetic dipole moment. The conversation also mentions using the derivative of the torque equation and substituting a variable (possibly a) in order to reach the desired result.
  • #1
ghoul
2
0

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.
ubsqgCZ.jpg
 
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  • #2
ghoul said:

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.
ubsqgCZ.jpg

Hi mister ghoul! :oldsmile:

What is ##\mathbf m##?
 
Last edited:
  • #3
I like Serena said:
i mister ghoul! :oldsmile:

What is ##\mathbf m##?
Hi,
I believe that m is magnetic dipole moment. m = Ia
 
  • #4
ghoul said:
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.
 

1. How do you define torque?

Torque is the measure of the force that causes an object to rotate around an axis or pivot point. It is calculated by multiplying the force applied to the object by the distance from the pivot point to the point where the force is applied.

2. What is the equation for calculating torque?

The equation for calculating torque is: T = r x F, where T is the torque, r is the distance from the pivot point to the point where the force is applied, and F is the force applied.

3. How is torque related to angular acceleration?

Torque and angular acceleration are directly proportional. This means that as the torque increases, the angular acceleration also increases. This relationship is described by the equation: T = I x α, where T is the torque, I is the moment of inertia, and α is the angular acceleration.

4. What is the role of magnetic field in torque calculations?

The magnetic field (B) plays a crucial role in torque calculations when dealing with magnetic objects. It is a vector quantity that describes the strength and direction of the magnetic force acting on an object. In the equation for torque, B represents the magnetic field strength and its direction determines the direction of the torque.

5. How can torque be used to prove that m x B?

To prove that torque is equal to m x B, we can use the equation for torque and substitute the relevant variables for a specific scenario. For example, if we are dealing with a charged particle moving in a magnetic field, we can calculate the torque by multiplying the charge (q) by the velocity (v) and the magnetic field strength (B). This will give us the same result as if we had calculated m x B, where m is the mass and B is the magnetic field strength.

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