# Comprehensive electromagnetic induction question

1. Mar 5, 2005

The magnetic field between the poles of an electromagnet is 2.6 T. A coil of wire is placed in this region so that the field is parallel to the axis of the coil. The coil has electrical resistance 25 , radius 1.9 cm, and length 15.0 cm. When the current supply to the electromagnet is shut off, the total charge that flows through the coil is 7.0 mC. How many turns are there in the coil?

I know that I have to use more than one equation but I've searched through my book for a couple hours now and nothing is helping. So far, I've picked up these equations:

I = (epsilon)/R = vBL/R
(epsilon) = -L (deltaI / deltat)
L = (mu0) n^2 (pi) r^2 l
flux = LI = (mu0) N I (pi) r^2

I tried to combine the equation for epsilon and self inductance (L) and came out with the wrong answers of 3.42E5 and 5.13E4. Ridiculously large numbers I'm sure. I would appreciate any insight =)

2. Mar 5, 2005

### Staff: Mentor

Actually, none of the four equations you chose are really appropriate for this problem. To get an idea of which equations you should look for (if you can't remember them), consider the following detailed description of what is physically going on here:

As the magnetic field produced by the electromagnet decreases from 2.6 T to zero, the magnetic flux through the coil decreases from some initial value, to zero. This change in flux induces an emf in the coil, which in turn causes a current in the coil. The net effect of this current, during the time it takes for the magnetic field to decrease to zero, is to cause a total of 7 mC of charge to flow through the coil.

From this description, I hope you can see that you need to know or find out the following relationships, and put them together:

1. How is the total charge that flows through the coil, related to the current through the coil?

2. How is the current through the coil related to the emf in the coil?

3. How is the emf induced in the coil related to the change in the magnetic flux through the coil?

4. What are the initial and final values of the magnetic flux through the coil?

You may need to introduce one or two other variables along the way, of course.

3. Mar 6, 2005