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Difficulty: MediumElectromagnetic Induction

When a strong bar magnet is dropped vertically through a long, hollow copper tube, its downward acceleration is equal to the acceleration due to gravity (gg) because copper is a non-magnetic material.

Answer: Answer

Answer

The statement is false. The magnet falls with an acceleration less than gg because induced eddy currents in the copper tube create an upward magnetic force that opposes the motion.
The statement is false because the relative motion between the falling magnet and the conductive copper tube induces eddy currents. According to Lenz's law, these induced currents set up a magnetic field that opposes the falling magnet's motion, creating an upward retarding force that reduces the downward acceleration to a value less than gg.

Step-by-Step Solution

1
Identify the physical interactions as the magnet falls through the tube.
The falling magnet creates a changing magnetic flux through the surrounding copper tube.
Relative motion between a magnetic field source and a conductor produces a time-varying magnetic flux in the conductor.
2
Apply Faraday's law of electromagnetic induction.
Electromotive force (e.m.f.) and circular eddy currents are induced in the conductive copper walls.
A changing magnetic flux induces electric currents in any closed conductive path.
3
Apply Lenz's law to determine the magnetic effect of the induced eddy currents.
The induced eddy currents produce a magnetic field that opposes the downward motion of the falling magnet, generating an upward magnetic force (FmagF_{\text{mag}}).
Lenz's law dictates that an induced current always flows in a direction such that its magnetic field opposes the change causing it.
4
Analyze the net force and resulting acceleration.
The net downward force is Fnet=mg−Fmag<mgF_{\text{net}} = mg - F_{\text{mag}} < mg, so the downward acceleration a=g−Fmagm<ga = g - \frac{F_{\text{mag}}}{m} < g.
The presence of an upward magnetic force reduces the net downward acceleration below the free-fall value of gg.

Key Concept

Lenz's Law and Eddy Currents in Conductors
Estimated Time:1m 0s
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Topics

Electromagnetic Induction

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