Electromagnetic Induction, AC Circuits, and Electrical Technologies

49 Eddy Currents and Magnetic Damping

Learning Objectives

  • Explain how eddy currents are produced and predict the direction of the induced current using Faraday’s and Lenz’s laws.
  • Describe how magnetic damping works and explain its applications in science, medicine, and engineering.

Eddy Currents and Magnetic Damping

In the previous section, we learned that an emf is induced whenever a conductor moves through a magnetic field or when a magnetic field moves relative to a conductor. If that conductor contains a closed path, the induced emf can drive circulating currents within the material itself. These circulating currents are called eddy currents.

Eddy currents are an important consequence of electromagnetic induction. Like any electric current, they produce their own magnetic field. According to Lenz’s law, this induced magnetic field always opposes the change that created it. As a result, eddy currents often generate a force that resists motion. This resistive effect is known as magnetic damping.

A simple demonstration is shown in Figure 49.1. A metal pendulum swings between the poles of a strong magnet. As the pendulum enters and leaves the magnetic field, changing magnetic flux induces eddy currents within the metal. These currents produce magnetic fields that oppose the pendulum’s motion, causing it to slow much more rapidly than it would due to air resistance alone. If the pendulum is made from an insulating material, almost no current is induced and the magnetic field has essentially no effect. If the pendulum contains slots cut into the metal, the damping is greatly reduced because the slots interrupt the paths available for the circulating currents.

The figure describes an experiment on exploring the effect of eddy currents. Part a of the figure shows a metal pendulum plate swinging between the pole pieces of a magnet. The pendulum is attached at one end to a pivot. Eddy currents are shown as small swirls on the surface of the plate. The oscillation is shown as damped by smaller displacement of the plate marked as S. Part b of the figure shows a slotted metal pendulum plate swinging between the pole pieces of a magnet. The pendulum is attached at one end to a pivot. Eddy currents are less effective. The oscillation is shown with a larger displacement of the plate marked as S, than the displacement in part a. Part c of the figure shows a non conducting pendulum plate swinging between the pole pieces of a magnet. The pendulum is attached at one end to a pivot. Extremely small currents are induced. The oscillation is shown with a larger displacement of the plate marked as S, than the displacement in part a.
Figure 49.1: A common physics demonstration device for exploring eddy currents and magnetic damping. (a) The motion of a metal pendulum bob swinging between the poles of a magnet is quickly damped by the action of eddy currents. (b) There is little effect on the motion of a slotted metal bob, implying that eddy currents are made less effective. (c) There is also no magnetic damping on a nonconducting bob, since the eddy currents are extremely small.

To understand why the force always opposes the motion, consider the conducting plate shown in Figure 49.2. As the plate enters the magnetic field, the magnetic flux through the metal increases. Faraday’s law tells us that this changing flux induces an emf, and Lenz’s law tells us that the resulting current must oppose the increase in magnetic flux. The induced current therefore circulates in the direction shown, producing a magnetic force that acts opposite the plate’s motion.

Once the entire plate is inside a uniform magnetic field, the magnetic flux through it remains constant. Because the flux is no longer changing, no eddy currents are produced and no magnetic damping occurs. As the plate exits the field, the magnetic flux decreases. A new eddy current forms in the opposite direction, once again producing a magnetic force that opposes the motion. Thus, whether the plate is entering or leaving the magnetic field, the induced force always resists its movement.

The figure shows a more detailed description of a conducting plate attached to a pivot oscillating between the pole pieces of a magnet. A cross section is shown in the figure. The direction of magnetic field of the magnet is toward the plane of the paper. The direction of force, current and magnetic field at two extreme positions of the pendulum are marked. The direction of B is always into the paper. Based on the direction of force, the current direction of the pendulum at the two ends is marked as per the right hand rule. The eddy current on the plate is in anti clock wise direction in the left end and clock wise direction in the right end.
Figure 49.2: A more detailed look at the conducting plate passing between the poles of a magnet. As it enters and leaves the field, the change in flux produces an eddy current. Magnetic force on the current loop opposes the motion. There is no current and no magnetic drag when the plate is completely inside the uniform field.

The slotted metal plate in Figure 49.3 demonstrates how engineers can reduce unwanted eddy currents. The slots interrupt the conducting paths, preventing large current loops from forming. Instead, only small localized loops develop, and neighboring loops often circulate in opposite directions so that many of their magnetic effects cancel. As a result, the magnetic damping becomes much weaker.

This same principle is widely used in engineering. Components such as transformer cores, electric motors, and generators are often constructed from thin insulated layers of metal, called laminations, rather than from one solid block. These layers greatly reduce eddy currents, improving efficiency and reducing unwanted heating. In contrast, some technologies intentionally take advantage of eddy currents. For example, induction cooktops generate eddy currents directly in the base of a cooking pot to produce heat, and magnetic braking systems use eddy currents to slow trains, roller coasters, and laboratory instruments without requiring physical contact.

The figure shows eddy currents induced in a slotted metal plate entering a magnetic field whose direction is shown as directed into the paper. The eddy currents are shown as small circular loops in line in each slot of the plate. The eddy currents are in such a way that neighboring loops in a single slot have currents in opposite direction. An enlarged view of two neighboring eddy currents in a slot is also shown.
Figure 49.3: Eddy currents induced in a slotted metal plate entering a magnetic field form small loops, and the forces on them tend to cancel, thereby making magnetic drag almost zero.

Applications of Magnetic Damping

Magnetic damping is valuable because it provides a smooth force that opposes motion without requiring physical contact between moving parts. Since the damping force is produced by eddy currents, it automatically becomes weaker as an object slows and disappears when the object comes to rest. This property allows magnetic damping to reduce unwanted motion without introducing friction or mechanical wear.

One important application is found in sensitive laboratory balances. Precision balances used in chemistry, biology, and medical laboratories must be extremely sensitive, so they are designed with very little mechanical friction. Without damping, however, the balance would oscillate for a long time before settling to its final reading. Magnetic damping solves this problem. A conducting disk attached to the balance moves through a magnetic field, producing eddy currents that quickly reduce the oscillations. As the balance approaches its equilibrium position, the eddy currents become smaller and the damping force naturally decreases to zero, allowing highly accurate measurements.

The figure shows a sensitive simple balance. The needle of this balance is held between the pole pieces of a magnet. The magnetic field direction is shown toward the plane of the paper. An enlarged view of the needle of balance and the magnets is also shown. The needle is shown as free to oscillate to and fro between the pole pieces of the magnet.
Figure 49.4: Magnetic damping of this sensitive balance slows its oscillations. Since Faraday’s law of induction gives the greatest effect for the most rapid change, damping is greatest for large oscillations and goes to zero as the motion stops.

Because eddy currents are produced only in conductors, recycling facilities can also take advantage of magnetic damping to separate metals from nonmetallic materials. As mixed waste slides down a ramp over a powerful magnet, conductive objects develop eddy currents and experience a magnetic drag force that slows their motion. Plastic, glass, wood, and other nonconducting materials are essentially unaffected, allowing the different materials to separate. Unlike simple magnetic separation, which works only for ferromagnetic materials such as iron and steel, eddy-current separation can also identify conductive nonmagnetic metals such as aluminum and copper.

A tipper truck unloading the trash down a ramp is shown. There is a rectangular block of magnet half way across the ramp with the north pole facing the ramp for separating metals from other trash by magnetic drag.
Figure 49.5: Metals can be separated from other trash by magnetic drag. Eddy currents and magnetic drag are created in the metals sent down this ramp by the powerful magnet beneath it. Nonmetals move on.

Eddy currents are also the operating principle behind metal detectors and magnetic braking systems. A portable metal detector contains a coil carrying an alternating current that continuously produces a changing magnetic field. When the detector approaches a metal object, eddy currents are induced in the object. These eddy currents create their own magnetic field, which alters the signal detected by a receiving coil and alerts the user to the presence of metal. Similar devices are widely used in airports, hospitals, archaeological surveys, and industrial quality control.

Several soldiers in an open field. One soldier is searching for explosives by scanning the surface using a metal detector.
Figure 49.6: A soldier in Iraq uses a metal detector to search for explosives and weapons. (credit: U.S. Army)

Magnetic braking uses the same physics on a much larger scale. Powerful permanent magnets are placed next to conducting metal fins attached to a moving train or roller coaster. As the fins pass through the magnetic field, eddy currents are generated in the metal. According to Lenz’s law, these currents produce magnetic fields that oppose the motion, creating a smooth braking force without any physical contact between the brake and the vehicle. Because there is no friction between moving parts, magnetic brakes experience very little wear and continue to operate reliably in wet, icy, or dusty conditions. However, since the braking force becomes smaller at lower speeds, conventional mechanical brakes are still required to bring the vehicle to a complete stop.

A roller coaster track with rows of magnets protruding horizontally that are used for magnetic braking in roller coasters.
Figure 49.7: The rows of rare earth magnets (protruding horizontally) are used for magnetic braking in roller coasters. (credit: Stefan Scheer, Wikimedia Commons)

Another everyday application is the induction cooktop. Beneath the ceramic cooking surface is a coil carrying a rapidly alternating current. This current creates a changing magnetic field that induces strong eddy currents in the base of a suitable cooking pot. The electrical resistance of the metal converts the energy of these currents into heat, warming the pot directly while leaving much of the cooktop surface comparatively cool. Because the process relies on magnetic induction, the cookware must contain a ferromagnetic material, such as iron or many types of stainless steel, so that the magnetic field couples efficiently into the pot.

Although eddy currents are useful in these applications, engineers often work to minimize them in electrical equipment such as transformers, electric motors, and generators because they waste energy as heat. Laminated metal cores and other specialized designs reduce unwanted eddy currents while preserving the desired magnetic fields, making these devices more efficient.

Section Summary

  • Changing magnetic flux in a moving conductor can produce circulating currents called eddy currents.
  • Eddy currents generate their own magnetic fields that oppose the motion or changing magnetic flux that created them, in accordance with Lenz’s law.
  • The opposing magnetic force produced by eddy currents is called magnetic damping. This force slows moving conductors without requiring physical contact or mechanical friction.
  • Magnetic damping is widely used in precision laboratory balances, magnetic braking systems, metal detectors, recycling facilities, and induction cooktops. In other devices, such as transformers and electric motors, unwanted eddy currents are minimized to improve efficiency.

Conceptual Questions

  1. Explain why magnetic damping might not be effective on an object made of several thin conducting layers separated by insulation.

  2. Explain how electromagnetic induction can be used to detect metals. Why is this technique useful in applications such as locating buried landmines, geophysical surveying, airport security screening, and detecting metallic foreign objects in industrial or medical settings?

Problems & Exercises

  1. Make a drawing similar to Figure 49.2, but with the pendulum moving in the opposite direction. Then use Faraday’s law, Lenz’s law, and RHR-1 to show that the magnetic force opposes the motion.

  2. A coil is moved through a magnetic field as shown in Figure 49.8. The field is uniform inside the rectangle and zero outside. What is the direction of the induced current and what is the direction of the magnetic force on the coil at each position shown?

    Figure shows the five stages of a single loop coil moved into and then out of a uniform magnetic field from left to right. It shows five stages a to e. The magnetic field is directed out of the page within a rectangular region. In stage (a), the single-loop coil is completely outside the magnetic field on the left. In stage (b), the coil is partially inside the magnetic field. In stage (c), the coil is completely inside the magnetic field. In stage (d), the coil is partially leaving the magnetic field. In stage (e), the coil is completely outside the magnetic field on the right.
    Figure 49.8: A coil is moved into and out of a region of uniform magnetic field.

Glossary

eddy current
a circulating current induced within a conductor when the magnetic flux through the conductor changes, such as when the conductor moves through a magnetic field or the magnetic field changes over time
magnetic damping
the resistive force produced by eddy currents that opposes the motion of a conductor through a magnetic field, slowing the object without physical contact
definition

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Introductory Physics for the Health and Life Sciences II Copyright © 2012 by OSCRiceUniversity is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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