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?
Best Answer
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.