# Magnet problem

1. Apr 15, 2004

### olympiad

hey, I have a tough time cracking this one
The other problem is:
Imagine a glass tube with steel rings around it which have a conductancy rho and a half diameter of R. they are spaced with a distance H.
inside the glass tube is a much smaller glass tube. Through it you drop a magnet with mass m and magnetic moment mu. the magnet will reach a final speed V quite soon. Explain with which factor the endspeed V will change if in five different experiments the five parameters(H,R,rho,M,mu) are doubled. You can neglect all form of friction, selfinduction and reciprocal induction.

I have a partial answer. You have to express v in the five parameters and then it is easy. If the speed is constant all height energy over a height H will be transfered into electric energy, so MHg=Pt with P the electric power and t the time that it takes to fall down a length of H. that time t is V/H. P is I^2*R.
So MHg=(V/H)*R*I^2. the problem is, how do you express I? mu=a*m^2 so I thought that the solution would be I=mu/(pi*R^2). (magnetic moment divided by area of one ring) But that can't be true because other rings have influence too, and now I just calculate the influence of one ring. Also, I don't take into account the distance between the rings. If you express V in this way H isn't in the formula, that can't be right. Help me please? thank you in advance.
olympiad

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