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Introduction
The aim of this experiment is to elucidate the Faraday's law of electromagnetic induction and
the Lenz's law.
Knowledge: Lenz's law, Faraday's law of electromagnetic induction,
The Activity
The experiment utilizes a conductive non-magnetic tube (Al, Cu, ...) and 10 neodymium
cylindrical magnets whose diameter is smaller than the bore of the tube. The experiment is
simple to execute, but one must be very careful when working with magnets. Your fingers
may get pinched when handling strong magnets! Moreover, magnets are rather brittle, and
when we let them quickly attract each other from a long distance they can break upon impact.
The experiment can be done in groups of 2-3 students, depending on the number of magnets
and conductive tubes available. Tubes of different materials can be used – e.g. copper,
aluminum or brass, and the results compared. First, let four magnets fall through the tube and
observe them. Then, let stacks of two to ten magnets to fall through the tube, and record their
transit times . Plot these values.
Task 1:
Explain why magnets are slowed down while falling through a conductive non-magnetic tube.
Auxiliary questions:
1.What do the Lenz's Law and the Faraday's law of electromagnetic induction describe? Try
to apply these laws to the experiment.
2.What are eddy (Foucault) currents?
3.Sketch the direction of currents induced in the conductive tube by a moving magnet.
4.Determine the direction of magnetic field lines generated by the induced currents (above
and below the falling magnet).
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Task 2:
Describe the relation between the number of magnets and the time of fall, and analyse the results of
your measurements.
Auxiliary questions:
1.How does the induced current affect the falling magnet?
2.How long will it take for the induced currents to fade away (and dissipate in heat).
3.How does the motion of a magnet stack depend on the distance between its poles (and the
induced currents)?
Explanation
Task 1:
A magnet falling through a conductive tube creates a time-dependent magnetic field, which in
turn induces Foucault (eddy) currents in the tube. The strongest currents occur around the top
and bottom ends of a stack of magnets because the field gradients are steepest there. Now,
consider an “observation” point located somewhere on the tube. As the field increases when
the bottom pole of the falling magnet approaches, in accordance with the Lenz's law a current
is induced that generates its own magnetic field which counteracts the magnet's field.
Consequently, the falling magnet experiences a force as if approaching a “virtual magnet”
with oppositely oriented poles, and this force acts as to slow down the motion. The situation
is similar at the top of the bunch, but the magnetic field now decreases with time, and the
induced currents create a field that adds to that of the falling magnet. This is as if the
additional field was created by yet another virtual magnet, this time with the same pole
orientation. As a result, the force acting on the upper end is decelerating the fall, too.
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Task 2:
If the distance between magnetic poles is large enough, the attraction between
the lower and the upper induced magnetic fields is weak. Adding more magnets
increases the mass of the stack, but the magnetic field remains essentially
unchanged. The result is shorter fall times for more magnets in the stack. If the
stack ends are closer to each other, the induced eddy currents will influence each
other. As they flow in opposite directions, they are mutually attenuated in the
overlapping region, and the fall time of the magnet is reduced. So it follows that
there must be an arrangement with a maximal fall time.
Summary
The temporal decay, or dissipation of eddy currents is caused by the resistance of
the conductor. The potential energy of the falling magnet is (partially) converted
into the magnetic field energy induced by the eddy currents. Because of the
conductor's resistance, this energy is eventually converted into heat.
As long as the conductive tube has a finite resistance, the magnet passes through because the
electromagnetic energy gets converted to heat.
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