What scale of magnetic field should I expect to be able to measure magnetic damping of a pendulum?

Question

As a practical investigation, I am attempting to measure the magnetic damping of a pendulum with a metal sheet as it swings through a magnetic field. My understanding of the phenomenon conceptually is this:

• As the pendulum swings through the field, the flux through it increases in one direction.
• By Lenz's Law, a current is induced which itself generates a magnetic field to oppose the change in flux.
• The magnetic field from the induced current is attracted to the existing magnetic field, opposing the momentum of the pendulum, eventually slowing it to a stop.

Here is a video example: Demonstration of magnetic dampening of pendulum

With my current set up, I have two solenoids side by side with the same polarity, and a rigid pendulum with a large aluminium sheet able to swing freely between them. With the solenoids on, and a magnetic field definitely being produced by each of the same polarity, I cannot observe any dampening effect.

I am wondering if anyone would have a rough idea of what sort of scale of magnetic field strength I might need in order to have an observable effect with my equipment - a stopwatch to measure the time taken to stop. Also may I have pointers towards estimating what sort of electrical power I would need through my solenoids to produce a certain field strength?

Answer 1

The principle you cite was the basic operating principle behind every analog speedometer and tachometer built up until the turn of the century. If you can get ahold of one of these and take it apart you will discover that the rotary shaft speed input turned a small magnet surrounded by an aluminum cup to which was also attached a hairspring and the speedo needle. the eddy current effect caused the aluminum cup to be dragged along with the rotating magnet with a force proportional to the rotation speed of the magnet, causing the needle to deflect against the restoring force of the spring.

Key to making this scheme work is the idea that the magnetic lines of force from the magnet must penetrate through the aluminum which makes me think that you have one of the solenoids wired in such a way that the sheet is being faced by magnets with the same pole adjacent to the sheets (N-to-N or S-to-S) which prevents the fields from going through the aluminum sheet. What you want is for the N pole of one solenoid to face the S pole of the other, so the field lines connecting them pass through the aluminum from one pole to the other.

Answer 2

What you perhaps not realised is that the MIT electromagnet is quite a substantial piece of apparatus?

The coils are connected so that the pole pieces have opposite polarity and you will note the iron core in the form of a U which increases the magnetic field strength between the pole pieces which are tapered to help increase the field.

To give you an idea Leybold is a manufacturer of such an apparatus and in their instruction sheet they state that for coils with $250$ turns carrying a current of $4\,\rm A$ and a pole piece separation of $5\,\rm mm$ a magnetic field of approximately $0.4\,\rm T$ is achieved. This is a very large magnetic field!
To achieve measurable damping in your experiment you probably do not need such a high field but I have given you an idea of the scale of the task facing your.
One thing I do suggest is that the swinging sheet be made of a reasonable thickness (to reduce its resistance and hence increase the magnitude of the eddy currents)of copper (which has a low resistivity).

In the modern world I would move to using Neodymium magnets or similar which produce very large magnetic fields and are not to expensive to buy.
You might try bending a steel, or better still iron, bar into the form of a $U$ and then add some Neodymium magnets.

There might even be enough damping if you use a wooden U and stick the magnets touching the wood to the wood.