2 Types Of Magnetic Potential Energy

• sawer
In summary, there are two types of magnetic potential energy equations: ##U = -\vec \mu \cdot \vec B## and ##U = \frac{1}{2} \int \mathbf{A} \cdot \mathbf{J} \, \mathrm{d}V##. The first equation is derived from the mechanical work done by rotating a magnetic dipole μ in a uniform magnetic field, while the second equation comes from the expression for field energy. The symbols used in these equations represent energy, magnetic moment, vector potential, current density, and volume. Further understanding of these concepts requires knowledge of electromagnetism.
sawer
There are 2 types of magnetic potential energy equations:
1. ##U = -\vec \mu \cdot \vec B##
2. ##U = \frac{1}{2} \int \mathbf{A} \cdot \mathbf{J} \, \mathrm{d}V##

- I have searched for the second equation, only can find some information in one web site. Do you know what their names are and differences?

- I see that second energy equation is derived from magnetic vector potential. But for the first equation, which potential equation is it derived from? Is it magnetic scalar potential?

Please explain the symbols: U, μ, A, J, V.

The first equation simply measures the mechanical work done by rotating a magetic dipole μ in a uniform magnetic feld.
The second equation comes from the expression for field energy $W=\int{\vec{H}\cdot\vec{B}}dV$. Im looking at the derivation from that to your equation given in Sommerfelds book (the only one I have handy at home) but you should find it in any upper level undergrad book.

sawer
Hesch said:
Please explain the symbols: U, μ, A, J, V.
Energy, magnetic moment, vector potential, current density, volume. If you don't know what they mean, youll need to study a little E&M first.

davenn
marcusl said:
The first equation simply measures the mechanical work done by rotating a magetic dipole μ in a uniform magnetic feld.
The second equation comes from the expression for field energy $W=\int{\vec{H}\cdot\vec{B}}dV$. Im looking at the derivation from that to your equation given in Sommerfeld`s book (the only one I have handy at home) but you should find it in any upper level undergrad book.

The first part looks good, but notice that the second equation contains the current density. I think $A \cdot J$ could be associated with the kinetic energy, and $H \cdot B$ the potential energy. These terms appear in the electromagnetic lagrangian as the magnetic components of A^J and F^*F . I'm not sure how the various tensor elements divide into potential and kinetic energy.

Last edited:

1. What are the two types of magnetic potential energy?

The two types of magnetic potential energy are magnetic dipole potential energy and magnetic field potential energy.

2. What is magnetic dipole potential energy?

Magnetic dipole potential energy is the potential energy stored in a magnetic dipole when it is placed in an external magnetic field.

3. How is magnetic dipole potential energy calculated?

Magnetic dipole potential energy can be calculated using the formula U = -m∙B, where U is the potential energy, m is the magnetic moment of the dipole, and B is the magnetic field strength.

4. What is magnetic field potential energy?

Magnetic field potential energy is the potential energy stored in a magnetic field due to the presence of a magnetic material or current-carrying wire.

5. How is magnetic field potential energy calculated?

Magnetic field potential energy can be calculated using the formula U = (1/2)∙μ₀∙χ∙H², where U is the potential energy, μ₀ is the permeability of free space, χ is the magnetic susceptibility of the material, and H is the magnetic field strength.

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