Fisica

INSTITUTE OF PHYSICS PUBLISHING Eur. J. Phys. 25 (2004) 463–468

EUROPEAN JOURNAL OF PHYSICS PII: S0143-0807(04)75775-X

Experiments with eddy currents: the eddy current brake
´ Manuel I Gonzalez
Departamento de F´sica, Universidad de Burgos, 09006 Burgos, Spain ı E-mail: miglez@ubu.es

Received 6 February 2004 Published 20 April 2004 Online at stacks.iop.org/EJP/25/463 (DOI:10.1088/0143-0807/25/4/001)
Abstract

A moderate-cost experimental setup is presented to help students to understand some qualitative and quantitative aspects of eddy currents. The setup operates like an eddy current brake, a device commonly used in heavy vehicles to dissipate kinetic energy by generating eddy currents. A set of simple experiments is proposed to measure eddy current losses and to relatethem to various relevant parameters. Typical results for each of the experiments are presented, and comparisons with theoretical predictions are included. The experiments, which are devoted to first-year undergraduate students, deal also with other pedagogically relevant topics in electricity and magnetism, such as basic laws, electrical measurement techniques, the sources of the magnetic field andothers.

1. Introduction

Eddy currents are one of the most outstanding of electromagnetic induction phenomena. They appear in many technical problems and in a variety of everyday life situations. Sometimes they are undesirable because of their dissipative nature (e.g. transformer cores, metallic parts of generators and motors etc). In many other cases, however, eddy currents are valuable [1](metal detectors, coin recognition systems in vending machines, electricity meters, induction ovens, etc). However, little attention is paid to eddy currents in many of the textbooks commonly used in introductory physics courses [1–3]: they are often dealt with only from a phenomenological point of view, and they are considered in some cases only as a topic for optional reading [1, 3]. Furthermore,most of the commercially available experimental setups concerning eddy currents treat only their qualitative aspects. This paper presents a set of laboratory experiments intended to help students better understand the phenomenon from a quantitative point of view. The experiments may be helpful to physics and electromagnetism students in first-year undergraduate courses.0143-0807/04/040463+06$30.00 c 2004 IOP Publishing Ltd Printed in the UK 463

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´ M I Gonzalez

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Figure 1. A sketch of the eddy currents in a rotating disc. The crosses represent a steady magnetic

field perpendicular to the plane of the disc. According to Faraday’s law, eddy currents appear in those points of the disc where the magnetic field increases or decreases.

2. Theoretical foundation

Inducedcurrents appear when electrical conductors undergo conditions of variable magnetic flux. In particular, we talk about eddy currents when bulk conductor pieces instead of wires are involved. There are two basic procedures to achieve such conditions: • exerting a time-varying magnetic field on a static piece; • exerting a steady magnetic field on a moving one. An example of the latter class will beinvestigated. It consists of a rotating metallic disc, which is subjected to the magnetic field present at the gap of an electromagnet. Eddy currents appear inside the disc and brake its rotation. This is the foundation of the electromagnetic braking systems used by heavy vehicles such as trains, buses or lorries [2]. Even in such a geometrically simple case, the pattern of eddy currents is complex.Figure 1 and [3] show simplified sketches of this pattern. It is easy, however, to obtain an approximate expression for the power dissipated by eddy currents. Since the magnetic field B is steady, the induced electric field in each point of the disc is given by E = v × B, where v is the velocity of that point [4]. Instead of measuring B directly, we will relate it to the excitation current Iex in the...