We have to find proportionality of the terminal velocity with the factors of the system:
Plot: a small dipole(mass m) with dipole moment μ is dropped in a long solenoid (radius r, Resistance RΩ) along it's axis. The gravity is acting downwards.
I found it to be v∝mRμ2r
Here is how:
The force in downward direction Fdown must be mg and in upward direction Fup must be magnetic force. Fup∝μIinducedr
Iinduced∝electric flux changeR∝μπr2vR
Flux change depends directly on the velocity, so added v in the numerator. But the expression is not correct. The proportionality on the r radius is not correct. I think there is a problem in the induced current factor.
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