# Force due to Eddy Currents

## Objective

To find the force due to eddy currents.

## Introduction

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.

## Apparatus

An aluminium plate and a mica board both pasted with similar paper, a strong magnet, glass slides to increase inclination, stop watch, scale.

## Procedure

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, \(mg\sin\theta=\mu mg\cos\theta+F_e\), 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.