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Faraday, Lenz, & Newton's Nightmare

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What is Newton's Nightmare?

The demonstration materials consist of a conducting nonmagnetic hollow metal tube, a small weight, and a small weight with a magnet within.

Begin by dropping the nonmagnetic weight through the tube. It should fall through quickly as the force of gravity alone is involved.

Next, the magnetic weight is dropped through the hollow tube. A significant delay occurs as the laws of electricity and magnetism slow the weight's descent through the tube.

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Demo equipment.

Newton's Nightmare physics.

There are several ways to look at the physics involved. We will focus on the following two principles of classical electromagnetism.

  1. A changing magnetic field produces a current.

  2. A current has a magnetic field associated with it.

The magnetic field B of a short bar magnet is shown on the right. The direction of the B field is represented by the arrows. By convention the magnetic field points from magnetic North to South.

As the magnet falls through the aluminum tube, the magnetic flux increases in the tube. Faraday discovered that a changing magnetic field leads to a flow of electric charges or current. Lenz specified the current's direction.

Bar magnet magnetic field.

Counter-clockwise current resulting from NS magnet entering tube.

Consider the case of a magnet falling with North pointed down. This produces a counterclockwise current as depicted in the diagram on the left.

Physics tells us that where there is a current, there is also a magnetic field. Therefore, a magnetic field is associated with our induced current. This induced magnetic field opposes that of the falling magnet.

A schematic on the right shows the directions. The velocity v of the magnet is downward, the change in the magnetic field is denoted by dB, and current is i.

Since the induced magnetic field opposes that of the falling magnet, it acts to reduce the magnet's gravitational acceleration as it begins falling through the tube.

Directions for i and B.
Directions as magnet passes point in tube.

As the falling magnet passes a position in the tube, the magnetic flux begins to decrease. This causes a current to flow in the direction opposite that of the entering magnet.

The magnetic field associated with this current is directed downward as in the left-hand side figure. Again, the magnet's acceleration is reduced since this second induced magnetic field tends to pull upward on the falling magnet.

Putting this all together we have a picture that looks like the figure on the left below. The sketch on the right gives the directions for a magnet falling with its South magnetic pole in the lead.

Falling N-S magnet produces opposing magnet fields to slow its progress through the tube.

N-S falling magnet.

Falling S-N magnet produces opposing magnet fields to slow its progress through the tube.

S-N falling magnet.

So ends the mystery, but not the fun of Newton's Nightmare!

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