How Do You Calculate Terminal Velocity of a Metal Ring in a Magnetic Field?

[accountdracula]

Homework Statement

I'm answering a question which describes a situation in which a metal ring is dropped through a magnetic field such that, when it falls, its area is perpendicular to the magnetic field.
I need to find its terminal velocity given:
Mass : 2.66 x 10^-4 kg
Magnetic flux density : 2.00 T
Radius : 2.00 cm
Resistance : 2.48 m(ohms)

Homework Equations

Emf = dBA/dt
V = IR
F = BILsin(theta)

The Attempt at a Solution

At terminal velocity, the magnetic force as a result of the ring's current must equal its weight:

mg = BIL

I'm confused about how to introduce v into the equation E.m.f = dBA/dt.
My thoughts were as follows:

If A is the area through which the ring moves in time dt then
A = pi r²vdt

e.m.f = (dBpi r²vdt)/dt
e.m.f = dBpi r²v

Dividing both sides by R :

I = (dBpi r²)/ R
I would then set this equal to mg / BL to find v.
However, in previous questions 'L' has always been a straight wire. Would you use the diameter of this metal ring or its circumference? My feeling is the circumference but I'm not 100% sure.
Also, is the way I've approached this question right?

 

[andrewkirk]

when it falls, its area is perpendicular to the magnetic field.

What does this mean? Do you mean that the disc that has the ring as boundary has a normal that is perpendicular to the mag field lines?

Is the magnetic field uniformly linear and self-parallel within the region of interest?

 

[accountdracula]

What does this mean? Do you mean that the disc that has the ring as boundary has a normal that is perpendicular to the mag field lines?

Is the magnetic field uniformly linear and self-parallel within the region of interest?

I mean the plane of the area of the metal ring is perpendicular to the plane of the magnetic field lines. The magnetic field is uniform. I don't have a clue what self parallel within the region of interest means.

 

[accountdracula]

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