# Demonstrations on Lenz's Law and Eddy Current

Following demonstrations on Lenz's law and eddy current can be performed at home or in the classroom.

## Magnet falling through a tube

When a magnet falls through a conducting tube, changing magnetic field is produced in the volume of the tube. Not only field is different at different places in the tube, it is also changing with time at any given place. Taking the long axis of the tube along the axis, the field change is largely in direction. A magnetic field changing in direction produces an electric field in the circumferential direction. The electric field lines are circular, coaxial with the axis. This field drives an electric current in the circumferential direction. The energy is lost in joule heating and this comes from the mechanical energy of the falling magnet. The magnet thus experiences an upward force slowing it down. The magnet takes an extraordinarily long time to fall through the tube.

### Procedure

Take a strong, short, cylindrical magnet. These are made of certain magnetic alloys like Niobium-iron-boron alloy. The size should be such that it can easily go through the aluminium tube you will be using. Take a similar looking piece of un-magnetized iron such as a nut or bolt and two or three more small objects made of different materials.

Keep the aluminium tube vertical and hold it in one hand. Drop different objects in the tube at the upper end and ask the students to estimate the time it takes for them to emerge from the other end. If your tube is 1 metre long, it will take only a fraction of second and estimates will be difficult to make. But they will have in mind that it is much less than a second.

Now drop the magnet in the same way. Students will be amazed to see that the magnet is not coming out. It takes very long time as compared to other objects. The time depends on the wall thickness of the tube and the strength of the magnet. For the tube that I use it is about 7 seconds, more than 25 times longer than the other objects.

It is instructive to understand where from the upward force come on the falling magnet. To the advanced students you can discuss the direction of current in the tube. The current goes in circular paths on the tube. Above the magnet it is in one sense and below the magnet it is in the other sense. Suppose the north pole of the magnet is up and the south pole is down. The current above the magnet is anticlockwise as seen from the top and that below is clockwise. The axial component of the magnetic field is outward in the portion above the magnet and inward below the magnet. Use to check that in both cases the force is upwards. Is it possible to design this experiment for balancing magnet in air? The answer is no!

Variant: Take a PVC pipe of approximately 1 m length. Make 1000 turns of insulated copper wire (SWG 36 is good enough) at multiple places along its length and connect a LED (1.5 V) at these points. Drop a strong magnet through the pipe. The LED will glow one after another as magnet moves. Now place a copper/aluminium pipe inside the PVC pipe and drop the magnet. The LED may not glow or become dimmer. Why? This experiment may be further extended but requires some expertise in electronics. Can we measure time interval (electronically) between glow of successive LED. This can be used to measure variation of magnet speed inside the tube. It can be given as project to electronics students.

Extension: Use solenoid in place of copper tube. Try with open and close ends of the solenoid.

## Slow down a rotating disc

There are many experiments to demonstrate Faraday's law of electromagnetic induction. Whenever a conductor is placed in a varying magnetic field or it moves under a magnetic field, emf is induced. If there are conducting paths available, currents start in the conductor which we call Eddy current. This experiment is one nice way to demonstrate eddy currents.

### Procedure

Mount the disc on the spindle of the motor. Connect the motor to the power source. Switch on the power so that the motor along with the connected aluminium disc starts rotating. Soon it will pick up a good speed. Now bring a magnet very close to the rotating disc. A pole should face the disc surface. The disc gradually slows down to almost a halt. Take the magnet a bit away. The disc again picks up speed.

The free electrons of the disc also move with the disc. When the magnet is kept near the rotating aluminium disc, the free electrons of the aluminium disc below the magnet experience magnetic force causing a motional emf in the conductor. This produces eddy currents in the disc. Energy is consumed in these currents putting more load on the motor. So the disc slows down.

## Electromagnetic damping

A magnet attracts pins, coins, nails etc because these materials are ferromagnetic. They contain domains in which magnetic moments of thousands of atoms are aligned in one direction. Aluminium is a paramagnetic substance and does not contain domains. So a magnet does not attract aluminium. However when motions are involved, situation could be different.

### Procedure

Put the aluminium plate below the given support. Hang the magnet from the support and adjust the length of the thread so that the magnet is slightly above (say about 1 mm) the plate. Let it come to complete rest. Now hold the plate from one side. Make sure that the plate does not touch the magnet. Keeping the plate on the floor/platform, pull it towards one side. What did you see? Was the magnet also pulled in the same direction in which the plate was pulled?

Hang the magnet from the given support. Do not put the aluminium plate right now. Pull the magnet to one side and release. It oscillates like a pendulum. Watch it for about 10 oscillations. See if there is a significant damping of amplitude. Stop the magnet. Put the aluminium plate below the hanging magnet. The magnet should not touch the plate and the separation should be small, say 1 mm. Now pull the magnet to one side and release. Look at the oscillations. Can you watch it for 10 oscillations? Oscillations are very quickly damped.

### Discussion

If aluminium is paramagnetic then why does it exert a force on the magnet to move it? This is because when the plate is set in motion, the free electrons in aluminium experience a force due to the magnetic field of the hanging magnet. This creates an emf which results in induced currents on the surface of the plate. Theses currents produced their own magnetic field and this magnetic field exerts force on the magnet to move it in the direction of plate's movement.

When the magnet moves, relative motion between the plate and the magnet is reduced. This is consistent with Lenz's law. Induced currents are produced due to relative motion between the plate and the magnet. The currents induced on the plate oppose this reason by dragging the magnet in the direction of plate motion.

As the magnet moves over the plate, magnetic field over the parts of the plate change in time. This changing magnetic field creates induced currents on the surface of the plate. These currents opposes the cause of the relative motion between the plate and the magnet. Thus the magnet slows down very quickly and almost stop in 2 or 3 oscillations.

## Force due to Eddy Current

When a magnet moves near a conductor, eddy currents are produced in the conductor. This current exerts a force on the magnet to oppose the relative motion. In the given set up, you will be able to measure this force in newton and find its dependence on the velocity.

### Procedure

You need an aluminium plate and a mica board both pasted with similar paper, a strong magnet, glass slides to increase inclination, stop watch and scale to perform this experiment.

Suppose the aluminium plate is kept at an inclination $\theta$ and a cylindrical magnet is allowed to slide down this incline. Because of eddy currents, the magnet soon acquires a terminal velocity $v$. As there is no more acceleration, Newton's second law gives, $mg\sin\theta=\mu m g\cos\theta+F_e$ , where $m$ is the mass of the magnet (given 6 grams) and $\mu$ is the friction coefficient between the magnet surface and the paper on which it slides. From this equation you can get the force $F_e$ due to eddy current.

Find the friction coefficient: Use the mica board given. Put the magnet on it, and increase the inclination till the magnet starts sliding. Determine the friction coefficient from $\mu=\tan\theta$. Repeat this at several places and several time to get an average value. Remember you need kinetic friction coefficient.

Finding force of eddy current: Use the aluminium plate and keep it at a certain inclination $\theta$. Check that the magnet slides. If it does not, friction is balancing the gravity. Increase the inclination.

Once it slides, measure the angle $\theta$ and the velocity $v$ of the magnet. Calculate the force $F_e$ due to eddy current. Repeat for various values of $\theta$ and plot a graph of $F_e$ versus $v$. Can you suggest an equation for this relation.

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