# Influence of Lorentz force on Eddy Current

A magnetic field exerts a force on a moving charge called Magnetic Lorentz force. How does this force work in case of eddy currents? The following is an extract from Wikipedia:

"Another way to understand the current is to see that the free charge carriers (electrons) in the metal sheet are moving with the sheet to the right, so the magnetic field exerts a sideways force on them due to the Lorentz force. The Lorentz force on positive charges F = q(v × B) is toward the rear of the diagram (to the left when facing in the direction of motion v). This causes a current I toward the rear under the magnet, which circles around through parts of the sheet outside the magnetic field, clockwise to the right and counterclockwise to the left, to the front of the magnet again."

In order for the charges to go in a circle, the magnetic Lorentz force should act as the centripetal force, correct? But this means that the direction of v and B should be perpendicular to each other. So, do eddy currents occur only when they are perpendicular?

If not, then how does the Lorentz force influence the motion of the charge carriers?

• $\vec{F} = q (\vec{v} \times \vec{B})$. The force acts as long as $v$ and $B$ are not parallel. Jan 6 '19 at 16:23

One idea may be that the magnetic term $$\overrightarrow{v}\wedge \overrightarrow{B}$$ is not the only one to put the charges in motion. In an electrical circuit, the electric field associated with the surface charges accumulating at the edge of the circuit must be taken into account. The generalized Ohm's law is written in this case $$\overrightarrow{j}=\gamma (\overrightarrow{E}+\overrightarrow{v}\wedge \overrightarrow{B})$$. The magnetic teme serves as an "emf source" in the region where $$\overrightarrow{B}$$ is intense and the electric field allows the return of the current when the field is zero. In a way, it does look like a Laplace Rail generator.
• Sorry, English is not my native language (I live in France). I should have said emf, (not the french term fem) as for a for a battery. When you move a rail in a magnetic field, an emf $vlB$ will appear and if the rest of the circuit is at rest, a current appear. It is a very simple linear generator. This experiment is know as "Laplace rail" in France. Jan 7 '19 at 20:14