# Energy of a magnetic dipole in an external B field

• kof9595995
In summary, Feynman's lecture on physics vol 2 explains that the "true energy" of a magnetic dipole (current loop) in an external B field is m*B, not -m*B. This is because extra work must be done to keep the current in the loop constant when pulling it from infinity to the final position. However, in statistical mechanics of magnetization, using U=m*B instead of -m*B leads to incorrect results, such as the belief that higher temperatures make it easier to magnetize a material. This is due to the fact that twice as much energy is needed to keep the current constant while it is moved. Additionally, the force on the loop is the same as the force on a permanent dipole

#### kof9595995

As in Feynman's lecture on physics vol 2, he showed that the "true energy" of a magnetic dipole(current loop) in an external B field is m*B, not -m*B. Basically the argument is if you want to pull a current loop from infinity to the final position, you must do extra work to keep the current in the loop constant. If you take this energy into account, the total energy will be m*B.
But in statistical mechanics of magnetization, if we use U=m*B instead of -m*B, we will get the opposite results,for example, we will get that the higher the temperature is, the easier to magnetize a material, which is obviously wrong.
How should I explain this?

The reason is (as RF said) that twice as much energy must be provided to a current loop to keep the current constant while it is moved. Although U=+m*B for a current loop, the force on the loop is given by F=+dU/dx so the force on the loop is the same on a permanent dipole. For a permanent dipole, U=-m*B, and F=-dU/dt, giving the same formula for the force. The magnetization in ferromagnetic materials is due to correlated electron spins and not current loops, which is why U=-m*B is apprlpriate.

it makes sense, thanks.

## What is a magnetic dipole?

A magnetic dipole is a physical object or system with two poles, a north pole and a south pole, that creates a magnetic field.

## What is an external B field?

An external B field is an external magnetic field that is created by a source outside of the magnetic dipole, such as a permanent magnet or an electric current.

## What is the energy of a magnetic dipole in an external B field?

The energy of a magnetic dipole in an external B field refers to the potential energy that is stored in the magnetic dipole due to its interaction with the external magnetic field.

## How is the energy of a magnetic dipole in an external B field calculated?

The energy of a magnetic dipole in an external B field can be calculated using the equation U = -m · B, where U is the potential energy, m is the magnetic moment of the dipole, and B is the strength of the external magnetic field.

## What factors affect the energy of a magnetic dipole in an external B field?

The energy of a magnetic dipole in an external B field is affected by the strength and orientation of the external magnetic field, as well as the magnetic moment of the dipole. Additionally, the distance between the dipole and the external field source can also affect the energy.