Eddy Currents

Introduction

How do roller coasters and trains control their speeds? One technique uses the speed-dampening power of eddy currents produced by moving magnets. Let’s see eddy currents in action.

Concepts

• Eddy currents
• Lenz’s law
• Magnetism

Materials

Safety Precautions

Although this activity is considered nonhazardous, please follow normal laboratory safety guidelines.

Disposal

The cylinders should be stored inside the aluminum tube, which is then sealed with the end caps.

Prelab Preparation

(Optional) Clamp the aluminum tube vertically to a support stand. Place a soft cloth towel beneath the tube to catch the cylinders as they fall through the tube (so they will not get scratched or dented). Alternatively, the aluminum rod can be held vertically with one hand and the cylinders can be dropped and caught with the free hand.

Procedure

1. Determine which cylinder is magnetic and which is nonmagnetic using steel paperclips or another magnet. (Initially, do not inform the students that the two cylinders are different).
2. Show the two identical-looking cylinders to the students by grasping the cylinders between your thumb and index finger so that the sides of the cylinders are visible (the black sheath is all the students see).
3. Drop the nonmagnetic cylinder through the vertically oriented aluminum tube.
4. Have students note the speed at which the nonmagnetic cylinder falls. (The nonmagnetic cylinder will fall consistent with normal gravitational acceleration.)
5. Drop the magnetic cylinder through the aluminum tube.
6. Have students note the speed at which this cylinder falls. (The speed of the magnetic cylinder is considerably slower than the nonmagnetic cylinder.)
7. Discuss the results with the students. Why does one cylinder fall more slowly than the other? Repeat the demonstration as many times as necessary.

Teacher Tips

• Have students look through the tube from the top to observe the magnetic cylinder as it falls. The cylinder falls slowly down the tube and actually reaches a terminal velocity as it tumbles. The cylinder reaches terminal velocity (constant speed) because the force of gravity and the dampening force of the eddy currents become balanced, resulting in zero acceleration. The cylinder is not slowed because of friction with the wall of the tube.
• When the students determine that one of the cylinders is magnetic, the students may believe the tube is magnetic too. Show them that it is not magnetic by demonstrating that the magnet and the tube do not attract each other. This reinforces the fact that an induced magnetic field is produced by the nonmagnetic metal tube when the magnet falls through it.

  Extension

• Practice spinning and balancing the magnet prior to the demonstration as shown in Figure 1.
• The aluminum can should be as thick-walled as possible. A soda can does not work well and has sharp edges when the entire top is removed. An aluminum catch bucket works well.
• This demonstration can be very dramatic if performed on an air table instead of on floating water.
• The right combination of sizes of parts is what makes this demonstration successful. The can needs to float on a high meniscus of water and therefore the bowl should be only slightly bigger in diameter than the can. If floating properly, the can should not touch the sides of the bowl. (A tea cup of the right size works well.)

Further Extensions

Another way to demonstrate Lenz’s Law is by “magically” spinning an aluminum can without touching the can.

1. Obtain a bar magnet.
2. Locate an aluminum can (as heavy gauge as possible) with a diameter about 1" greater than the length of your bar magnet. An aluminum density catch bucket works well. (If the top of the can needs to be removed, do it carefully.)
3. Tie a thread tightly around the center of the bar magnet so that it can be spun in a circular fashion as shown in Figure 1.
   {12920_Procedure_Figure_1}
4. Locate a container (e.g., finger bowl, regular bowl) that is about 1" greater in diameter than the aluminum can.
5. Place the bowl in the center of a spill tray.
6. Fill the bowl to its very top with tap water until it can not hold any more water. A “bulging” bowl of water is ideal.
7. Carefully float the aluminum can open-side-up on top of the water. The final setup should look like Figure 2.
   {12920_Procedure_Figure_2}
8. With the magnet hanging outside the can, start the magnet spinning on the hanging thread. Spin and balance the magnet so it is spinning in a level, even fashion. Then slowly lower the spinning magnet down inside the lip of the can, being careful to not touch the side of the can. (This might take a little practice and a steady hand.)
9. Watch what happens to the floating can. What direction does it spin compared to the magnet? What happens when the thread is completely unwound and the magnet spins in the opposite direction?

Discussion

During the nineteenth century, electricity and magnetism were unusual and not well understood phenomena and many scientists devoted their time experimenting on these wonders to determine their properties. In the course of their research, scientists, such as Michael Faraday, Joseph Henry, Andre-Marie Ampere and Heinrich (H.F.E.) Lenz, discovered that magnetic fields and electric currents were closely related. Through observation and experimentation scientists determined that an electric current in a wire creates a magnetic field around the wire, and also that a changing magnetic field can generate (induce) an electric current in a wire. It is this changing magnetic field that is responsible for the creation of eddy currents.

Michael Faraday determined that the current induced in a closed conducting wire loop due to a change in the magnetic field’s strength or direction running through the closed loop is equal to the rate of change of the magnetic field. This is known as Faraday’s law. The strength and direction of a magnetic field is also known as the magnetic flux. The induced current in the loop does not depend on how large the magnetic field is initially or how large the magnetic field is after the change. It only depends on how quickly the magnetic field changes in strength, direction or both.

Heinrich Lenz further investigated Faraday’s law and discovered that the induced current in the loop will travel in a particular direction to satisfy the conservation of energy principle. Since the induced current produced by the changing magnetic field also produces its own magnetic field, the current will travel in the direction around the loop so as to maintain the original magnetic flux through the loop (see Figure 3). This is known as Lenz’s law. For example, if the magnetic field through the closed loop decreases, the current induced in the loop will travel so that its magnetic field will increase the magnitude through the loop and therefore maintain the initial magnetic flux. The direction of the magnetic field from a current traveling around a loop can be determined using the “Right-Hand Rule.”

By pointing the thumb on your right hand in the direction of the current around the loop, your fingers will curl in the direction of the net magnetic field produced by this current (see Figure 4). In the Eddy Current Demonstration, a cylindrical magnet is dropped through a metal conducting tube. The tube is essentially a linear series of thin, closed conducting loops. As the magnet approaches these loops, it induces eddy currents in these loops that produce a magnetic field in the opposite direction to the magnetic field of the magnet (to maintain the original magnetic flux—which was zero). The opposing magnetic fields create an upward force on the magnet as it falls through the tube. Once the magnet passes through the thin loop and the magnetic field begins decreasing in this loop, a current is induced in the closed loop that travels in the opposite direction compared to when the magnet was approaching the loop. This current then produces a magnetic field that is oriented in the same direction as the falling magnet. This results in an attractive upward force on the magnet. The upward forces dampen the speed at which the magnet falls. The force of gravity and the upward force will eventually become balanced causing the magnet to reach a constant velocity (terminal velocity) inside the tube (see Figure 5).

References

The Spinning Can: Lenz’s Law Demonstration; Flinn Scientific: Batavia, IL, 2000.

Tipler, Paul A. Physics for Scientists and Engineers, 3rd Ed., Vol. 2; Worth Publishers: New York, 1990; pp 840–848.