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

# Uniform Magnetic Field does not Exert Force on a Magnet

## Introduction

A magnet is made of collection of small magnetic dipoles. Each dipole can be treated as a combination of north and south pole of equal strength. For the same magnetic field B and same strength of the two poles, the forces by the field on the two poles will have the same magnitudes. As the directions are opposite, the net external force will be zero on each dipole and hence on the magnet. Is this experiment you see it in real time.

## Apparatus

A solenoid, DC source, a small cylindrical magnet, a sensitive spring balance, arrangements for hanging the magnet and keeping the solenoid vertically.

## Procedure

1. Fix the spring balance on a vertical stand. From the hook, suspend a nut using a piece of thread and stick the magnet to this nut.
2. Read the reading on the spring balance. It gives the weight of the nut and the magnet. Note that the spring balance is graduated in newtons.
3. Put the solenoid in vertical position at a height so that the magnet is inside the solenoid but close to its upper end.
4. Connect the solenoid to the DC source (switch off). Switch on the source. If the magnet jumps up, reverse the polarity of the source.
5. Switch on the source and note that the magnet goes inside. Note the reading on the spring balance. How many newtons of force is exerted by the solenoid on the magnet?
6. Now change the height of the spring balance so that the magnet lies near the middle of the solenoid.
7. Switch on the source. Does it goes further down?

## Discussion

The magnetic field in an infinite solenoid is $$\mu_0 n i$$, independent of the distance. For a finite solenoid with length several times the diameter, of the reading, the field will be nearly uniform in the central region but non uniform near the ends. The non uniform field exerts net force on the magnet which is shown on the spring balance.