Magnet dropping through a loop

In summary, a permanent magnet with mass m and dipole moment μ is initially located on the vertical axis of a stationary, conducting, non-magnetic ring with a radius a, resistance R, and inductance L. At time t=0, the magnet is released and the equation of motion can be written down. The retarding force acting on the magnet is due to the magnetic flux generated by the induced current passing through the loop, according to Lenz' Law. To evaluate the equation of motion, the work done to create the current in the loop must be equal to the thermal energy generated in the loop, in order to conserve energy.
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A permanent magnet of mass m is located on the vertical axis of a stationary, conducting , non-magnetic ring for a long time. The ring has a radius a, resistance R and inductance L.At time t=0 the magnet is released. Suppose the magnet has dipole moment [tex]\mu[/tex]z. Write down the equation of motion.

Is the retarding force due magnetic flux generated by the induced current passing through the loop? If that is the case how do I evaluate the equation of motion of the magnet?
 
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  • #2
Consider Lenz' Law. Energy must be conserved, so the work done to create the current in the loop must equal the thermal energy generated in the loop.
 
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1. What is the phenomenon behind a magnet dropping through a loop?

The phenomenon behind a magnet dropping through a loop is electromagnetic induction. When a magnet moves through a conductor, it creates a changing magnetic field, which in turn induces an electric current in the conductor.

2. How does the shape and size of the loop affect the speed of the falling magnet?

The shape and size of the loop do not have a significant effect on the speed of the falling magnet. The main factor that affects the speed is the strength of the magnetic field and the distance between the magnet and the loop.

3. Can the magnet drop through the loop if the loop is made of a non-conductive material?

No, the magnet will not induce an electric current in a non-conductive material, so it will not drop through the loop. The loop must be made of a conductive material for the phenomenon to occur.

4. Why does the magnet slow down as it goes through the loop?

The magnet slows down as it goes through the loop because the induced current creates a magnetic field that opposes the magnet's motion. This opposing force is known as Lenz's Law and it acts to slow down the magnet's movement.

5. Is the magnet dropping through a loop an example of perpetual motion?

No, the magnet dropping through a loop is not an example of perpetual motion. The energy used to move the magnet through the loop comes from the force of gravity, and eventually, the magnet will come to a stop due to friction and other factors.

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