# Homework Help: Inducing EMF by changing area

1. Nov 8, 2015

### accountdracula

1. The problem statement, all variables and given/known data
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
Resistance : 2.48 m(ohms)

2. Relevant equations
Emf = dBA/dt
V = IR
F = BILsin(theta)

3. 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?

2. Nov 8, 2015

### andrewkirk

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?

3. Nov 9, 2015

### accountdracula

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.

4. Nov 9, 2015

Bump