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Re: [Phys-l] drop a metal cylinder through a solenoid



A) The dominant effect of the magnetism will be eddy-current damping,
yet the question asks about "period".

You're right. I meant damping. Specifically if we define the mechanical energy to be KE + gravitational PE of the bob, what fraction of the initial mechanical energy has been dissipated away by induction as a function of time?

In case (1) there is a huge amount of eddy current damping, while in
case (2) there is almost none.

Okay, agreed. Can one be quantitative about case 2? You say very little mechanical energy is lost. But how much - what do we need to know to answer?

Suppose the metal bob is a cube of side d. Magnetic field is B. Bob is initially raised up to 90 degrees, a distance of L above the lowest point of its swing (ie. the arm length).

I would start by saying motional emf is v*B*d where v is speed of the bob at any point. If the damping is small, v isn't much different than regular pendulum, sqrt(2*g*L*cos(theta)) where theta is angle of pendulum relative to vertical.

Now it gets trickier. That emf must correspond to some charge separation between opposite edges of the bob (edges of area d^2 that are a distance d apart). How much? Perhaps I can model it as a parallel-plate capacitor. And then I have to figure out how much energy it cost to drive that charge there - probably depends on the resistivity of the metal bob, but that will only get me power; I'll also need the drift velocity to get the time during which the charges move. Hmm... it's getting rather involved. Is there any simpler way to figure out the energy lost to induction? (I don't have any goal in mind here with any of my posts. I'm just exploring.) -Carl