Question

The motion of a copper plate damped when it is allowed to oscillate between the two poles of a magnet. What is the cause of this damping?

Answer 1

Hint: We know that according to Lenz’s law in electromagnetism, the induced electric current flows in a direction such that the current opposes the change that induced it. It can be expressed as - \[ \in = - N\dfrac{{\partial {\phi _B}}}{{\partial t}}\] and the eddy current opposes the motion and brings the pendulum to rest. Opposing direction is an attempt of the system to resist the changes that are taking place like relative motion of charges w.r.t. surrounding.

Complete step by step answer:
We know that according to Lenz’s law in electromagnetism, the induced electric current flows in a direction such that the current opposes the change that induced it. This can be expressed as - \[ \in = - N\dfrac{{\partial {\phi _B}}}{{\partial t}}\]. Here, \[ \in \] is induced emf, \[N\] is the number of turns in the coil \[\partial {\phi _B}\] is the change in magnetic flux and \[\partial t\] is the change in time.
When the copper plate is oscillating in the magnetic field between the two poles of the magnet, there is a continuous change in the magnetic field. This generates magnetic flux linked with the pendulum. The induced magnetic flux produces an eddy current is induced and this eddy current is set in the copper plate which tries to oppose the motion of the pendulum that brings the damping in the oscillation of the copper plate pendulum in between the two poles of the magnet. We can say that the produced eddy current opposes the motion of the pendulum and brings it to the rest. Thus, the copper plate is damped.

Additional information:
The eddy current is also known as circulating current, this will occur when the conductor experiences a change in the magnetic field. These currents are not responsible for doing any useful work but it produces a loss \[{I^2}R\] in the magnetic material known as eddy current loss.

Note:
One can assume that the eddy current will give more kinetic energy to the copper plate and because of excess kinetic energy, the pendulum may break and this causes damping of the pendulum. But we know that the eddy current opposes the motion and brings the pendulum to rest.