Can magnetic dipoles have potential energy?

AI Thread Summary
Magnetic dipoles can have potential energy despite magnetic forces not being conservative. The potential energy U for a magnetic dipole is expressed as -m . B, where m is the magnetic moment and B is the magnetic field. While magnetic forces can accelerate a dipole, leading to changes in kinetic energy, this does not violate energy conservation laws. The interaction with a non-uniform magnetic field results in a change in potential energy, represented as delta mB. Therefore, magnetic dipoles can indeed possess potential energy in specific contexts.
averin
Messages
1
Reaction score
0
People say U for a magnetic dipole is -m . B
But why can magnetic dipoles have potential energy, if magnetic forces are not conservative?

Thanks!
 
Physics news on Phys.org
averin said:
People say U for a magnetic dipole is -m . B
But why can magnetic dipoles have potential energy, if magnetic forces are not conservative?

Not being conservative for B does not mean violation of the energy conservation law. In case of a single charge, its kinetic energy is conserved. In case of magnetic dipole, the external non uniform magnetic field can accelerate the dipole thus increase its kinetic energy. The corresponding potential energy change is delta mB.

Bob_for_short.
 
This is from Griffiths' Electrodynamics, 3rd edition, page 352. I am trying to calculate the divergence of the Maxwell stress tensor. The tensor is given as ##T_{ij} =\epsilon_0 (E_iE_j-\frac 1 2 \delta_{ij} E^2)+\frac 1 {\mu_0}(B_iB_j-\frac 1 2 \delta_{ij} B^2)##. To make things easier, I just want to focus on the part with the electrical field, i.e. I want to find the divergence of ##E_{ij}=E_iE_j-\frac 1 2 \delta_{ij}E^2##. In matrix form, this tensor should look like this...
Thread 'Applying the Gauss (1835) formula for force between 2 parallel DC currents'
Please can anyone either:- (1) point me to a derivation of the perpendicular force (Fy) between two very long parallel wires carrying steady currents utilising the formula of Gauss for the force F along the line r between 2 charges? Or alternatively (2) point out where I have gone wrong in my method? I am having problems with calculating the direction and magnitude of the force as expected from modern (Biot-Savart-Maxwell-Lorentz) formula. Here is my method and results so far:- This...

Similar threads

Back
Top