# Why are there 2 definitions of Magnetic Moment?

• tessx
In summary, the conversation is about the confusion and questions surrounding the magnetic moment and its different expressions. The first equation, \mu = IA, is a fundamental definition of the magnetic moment, while the second equation, \mu = \frac{m v^2}{2 B}, is a derived equation specific to the context of space plasmas. The second equation relates the energy of a moment in a field to the movement of particles.
tessx
Hello everyone, this is my first post at Physics Forums!

I am trying to understand electromagnetism, and when it comes to the magnetic moment, when reading around I see $$\mu = IA$$ where A is area of a loop, which is an expression I can sort of understand. But when reading about magnetic drifts (I am a little confused for the moment) I see $$\mu = \frac{m v^2}{2 B}$$. I am sure both refer to the same value but I cannot visualise how.

Would someone be kind enough to explain this to me?

Thank you!

Tessx

Last edited:
I don't remember ever seeing your second equation. If you found it on the Web, can you give us a link to it, or if in a book, which book it was and what the context of the equation was? (What was the book discussing at that point?)

jtbell,

The context of the second equation is in space plasmas, describing the ratio between perpendicular particle energy and magnetic field.
I found the equation in a book called "Basic Space Plasma Physics" by Baumjohann W. and Treumann R. A., Imperial College Press 2004.
What I don't get is how do they get to this expression, and how does it "fit" with the other one (=IA).

Unfortunately, I don't know squat about space plasma physics. Maybe someone who does know something about it will see this.

I'd say that your second equation is a derived equation appropriate to a particular problem. Note that (mv^2)/2 is kinetic energy and mu B has units of energy, so this equation relates the energy of a moment in a field to some situation where particles are moving. It is not a fundamental definition of moment like the first equation.

## 1) Why are there two definitions of Magnetic Moment?

There are two definitions of Magnetic Moment because they describe different properties of magnetic materials. One definition is based on the torque experienced by a magnet in a magnetic field, while the other is based on the magnetic field strength and the area of the coil.

## 2) What is the difference between the two definitions of Magnetic Moment?

The main difference between the two definitions of Magnetic Moment is the way they are measured. The first definition, also known as the mechanical definition, is based on the force experienced by a magnet in a magnetic field. The second definition, known as the electromagnetic definition, is based on the strength of the magnetic field and the area of the coil.

## 3) Which definition of Magnetic Moment is more commonly used?

The electromagnetic definition of Magnetic Moment is more commonly used in scientific studies and applications. This is because it is easier to measure and can be used to describe the behavior of magnetic materials in various situations.

## 4) Why do we need two definitions of Magnetic Moment?

Both definitions of Magnetic Moment have their own advantages and are used to describe different properties of magnetic materials. The mechanical definition is useful for studying the behavior of magnets in a magnetic field, while the electromagnetic definition is more applicable for understanding the magnetic properties of materials.

## 5) How are the two definitions of Magnetic Moment related?

The two definitions of Magnetic Moment are related through the concept of torque. The mechanical definition is based on the torque experienced by a magnet in a magnetic field, while the electromagnetic definition is based on the torque produced by the magnetic field on a current-carrying coil. This relationship helps to bridge the two definitions and allows for a better understanding of magnetic materials.

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