Eddy currents and current induction questions

[waterbottle12]

Homework Statement

A solenoid is connected to a power supply and a ring of metal is sitting on top of the
solenoid. When the power supply is turned on the ring jumps up off the solenoid.
a) Suppose that when you look down at the solenoid from above. The current due to the
power supply is going around the solenoid in a clockwise direction. Use Lenz' law to
determine the direction of the induced eddy current in the ring. Explain your reasoning.
b) Explain, in terms of the force on a current in a magnetic field, why the force on the
ring due to the interaction between the induced current and the magnetic field of the
solenoid is up.
c) If the current through the solenoid is suddenly reversed in direction, is the force on
the ring up or down? Explain.

Homework Equations

The Attempt at a Solution

a. I don't know if I'm doing RHR correctly but I said that since the current is clockwise, the magnetic field is downwards. By lenz law, the eddy current needs to produce a field that would oppose this downwards increase in flux. I did RHR again and said eddy current is counterclockwise.
b. The force is upwards because the magnetic field exerts a force on the induced current...?
but I thought that the force (by RHR) is supposed to be perpendicular to the current and field?
c. Not sure...but I would imagine it just being in the opposite direction (downwards) if the current is reversed (too simple reasoning?)

Homework Statement

When a magnet is dropped down a vertical aluminum tube, the kinetic energy of the
magnet as it exits the bottom of the tube is only about 10% of the change in gravitational
potential energy as the magnet moved from the top of the tube to the bottom. What
happened to the missing energy? What is the final form of the missing energy? Explain.

Homework Equations

The Attempt at a Solution

I said that the missing energy is lost as electrical energy...like current since the magnet going through the tube induces a current. I saw this demonstration in class and the magnet came out very slowly...maybe some of the energy was an upward force that opposed gravity and slowed the magnet's motion?

 

[anathema]

I'm not sure about the final form of the missing energy though.

Hello there,

a) Your reasoning for the direction of the induced eddy current is correct. By Lenz's law, the eddy current will produce a magnetic field that opposes the change in flux caused by the clockwise current in the solenoid. This means that the eddy current will produce a magnetic field in the opposite direction, counterclockwise.

b) The force on the ring is indeed perpendicular to both the current and the magnetic field. However, the direction of the force is determined by the cross product of the two vectors. In this case, the direction of the force is upward because the current and the magnetic field are in opposite directions.

c) You are correct, the force on the ring would be in the opposite direction (downward) if the current is reversed. This is because the direction of the magnetic field would also be reversed, so the cross product of the current and magnetic field would still result in an upward force.

For the second forum post, you are on the right track. The missing energy is indeed converted into electrical energy through the induction of a current in the aluminum tube. This current creates a magnetic field that opposes the motion of the magnet, thus slowing it down and converting its kinetic energy into electrical energy. The final form of the missing energy is indeed electrical energy.

I hope this helps! Let me know if you have any other questions.