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Two plates of the same size and metal hang as pendulums between the poles of a magnet…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Two plates of the same size and metal hang as pendulums between the poles of a magnet. Plate A is solid. Plate B has several slots cut in it, from the lower edge upwards. Each plate is pulled aside and let go. Plate A stops after less than one swing. Plate B swings several times. Explain the difference. Then say where the energy of the swing of plate A goes.
Need a reminder? The key ideaShow
A changing flux drives eddy currents in a solid conductor. They oppose the change (Lenz's law), so a moving conductor is braked, and the work done becomes heat. At a steady speed, the drag equals the weight in a fall, , and the heat each second is . A disc of radius and thickness in a field changing at loses . In a thin sheet, .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The solid plate. As plate A moves in the field, the flux through loops in the plate changes. Large eddy loops form. They carry a large current, and the force on that current opposes the motion. So the plate is braked at once.
Step 2. The slotted plate. The slots cut the large loops. Each loop must stay inside one tooth. It encloses less flux, so its emf is smaller. Its path is longer and narrower, so its resistance is larger. The current is much smaller, and so is the braking force. Plate B swings freely for many swings.
Step 3. The energy. The swing energy of plate A becomes heat in the plate, in the eddy currents. The plate warms up a little.
Watch out. The slots do not stop the eddy currents completely. They only make them small.
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