IIT JEE Physics (1978-2018: 41 Years) Topic-wise Complete Solutions

# A Magnet Falling Through Conducting Tube

## Objective

To study the effect of eddy currents when a magnet falls through a conducting tube

## Introduction

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 $$z$$ axis, the field change is largely in $$z$$ direction. A magnetic field changing in $$z$$ direction produces an electric field in the circumferential direction. The electric field lines are circular, coaxial with the $$z$$ 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.

## Apparatus

A copper or aluminium tube, a strong magnet

## 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.