# How to find the direction of an eddy current?

Suppose there is a magnetic field going from left to right. Suppose a thin sheet of metal conductor (e.g. a 1m*1m square) is dropped through the magnetic field such that the plane of the conductor is PERPENDICULAR to the magnetic field.

Now I know that by Faraday's Law, there will be an induced emf that will induce eddy currents in the conductor which oppose the motion of it by Lenz's Law. However, I have no idea which way the eddy currents are flowing, i.e. clockwise or anticlockwise.

Does there exist a simple hand rule which can predict the direction of eddy current?

The first thing to note is that if the loop is moving through a uniform magnetic field the induced emf and hence the induced current is zero as there is change in the magnetic flux through the loop.

The first thing you need to decide is whether or not the magnetic flux through the loop is increasing or decreasing.
The use Lenz's law which states that the induced current will be in such a direction as to oppose the motion producing it.
So the direction of the current will try and either decrease the magnetic flux through the loop.
You can use the right hand grip rule to decide on the direction of the induced current.

I am not so good at 3D diagrams so here is one with the external magnetic field into the screen and the loop moving down the screen.
I also have drawn a loop rather than a plate so the induced currents will flow in the plate in the direction shown in the diagrams probably more in the region where the magnetic flux is changing.

So the eddy currents in the conducting plate will flow anti-clockwise in the left hand diagram and clockwise in the right hand diagram.

An eddy current is generated due to Lenz's law, so the current will produce a magnetic field in order to oppose the change that created it right. So for example, You move a metal sheet into a magnetic field, a current will be created so as to OPPOSE this force moving it into the field. So the force that the eddy current creates will be to the left. Using your right hand palm rule. Fingers point into the page since magnetic field is into the page, and palm points to the left....so your thumb points up. Now eddy currents whirl around in a circle, so imagine the current like a circle. Your thumb pointing up means that the current is going anticlockwise.

You may get confused as to whether your thumb is pointing up at the 3 o clock position or the 9 o clock position of the circle. But since the metal sheet is moving from left to right, it is the 3 o clock position that the current is pointing up in.

as a thought

$$\nabla \times j = M$$

$$\nabla \times M = j$$

this current density has three manifestations shown in amperes material derviation:

$$\nabla \times B = \mu_0(j_f + j_p + j_m) + \epsilon_0 \frac{\partial E}{\partial t}$$

Current due to change in polarisation

$$j_p = \frac{\partial P}{\partial t}$$

Current due to rotation of magnetisation

$$j_m = \nabla \times M$$

Current due to p.d

$$j_f = I$$

$$\therefore \nabla \times \frac{B}{\mu_0} - M = j_f + \frac{\partial( \epsilon_0 E + P)}{\partial t}$$

as $$\epsilon_0E + P = D$$

and

$$\frac{B}{\mu_0} - M = H$$

then

$$\nabla \times H = j_f + \frac{\partial D}{\partial t}$$

By going in and out of the free space and material representations of Ampere's Law, you can see that a magnetic field next to a material would produce such a current. i.e the the curl of H creates a change in the displacement current or creates a magnetic current density.