- #1

FelaKuti

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## Homework Statement

A cylindrical magnet with its axis vertical provides a radial magnetic field. A thin, circular aluminium ring that is co-axial with the magnet falls through the magnetic field.

By finding an expression for the current in the ring when it is falling at the speed v, or otherwise, determine the terminal velocity of the ring if the magnetic flux density at the circumference of the ring is 2.00T, and the ring has mass 2.66 x 10^-4 kg, radius 2.00 cm and R = 2.48 mOhms

Q from here: https://isaacphysics.org/questions/ring_drop?board=6e219139-c944-4b22-9a12-9a560fd199ce

## Homework Equations

induced emf = NdΦ/dt

W = mg

V = IR

Φ = BA

F = BIL

## The Attempt at a Solution

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If it reaches terminal velocity then weight downwards must equal magnetic force upwards. To work out magnetic force I need an equation for the induced emf so V = NdΦ/dt. I calculated the change in magnetic flux linkage as pir

^{2}* v * dt * B.

Dividing by dt gives the rate of change of flux linkage which is pi * r

^{2}* v * B which equals induced emf V.

Divide the LHS by R to give an equation for current, which I put into BIL and equate to mg. But I have a length l which I don't know how to eliminate whilst still being able to work out v, so I think my method here is wrong.