# Homework Help: Induction and EMF

1. Nov 24, 2007

### captain.joco

1. The problem statement, all variables and given/known data
In a ring of radius R, there is current I flowing in the counterclockwise direction as viewed from above. A small ring of radius r is on a common axis and is a hight z above the current carrying ring, where z>>R. The small ring moves up with velocity v. Calculate the emf in the upper ring and the direction of the induced current. It can be assumed that the ring is sufficiently small so that the magnetic field across it's area is constant.

2. Relevant equations

3. The attempt at a solution
So E= - dΦ/dt
Φ = B*A ( since the magnetic field across it's area is constant ).
A = π*r*r
B= (μIR^2) / [ 2 ( R*R + z*z )^3/2 ] but since z>>R we can use the approximation
B= (μIR^2) / (2z^3)

Now i know I need to do the -dΦ/dt but I am getting confused ( how to do it? ).

2. Nov 24, 2007

### G01

In order to do the derivative you need to have time involved. The only quantity in that expression for the flux that depends on time is z, correct? Is there any way to get z in terms of time?

HINT: Have you used the velocity, v, yet?

3. Nov 24, 2007

### captain.joco

So will the emf be A* (μIR*R/2) * 3( v^3 * z^4 ) or I did it very very wrongly..

4. Nov 24, 2007

### G01

$$\Phi=\frac{\mu IR^2A}{2z^3}$$

Then, remember that: v = z/t.

Can you use the last expression to remove z from the first?

5. Nov 24, 2007

### captain.joco

Sorry I made a typo.. should have been A* (μIR*R/2) * 3/( v^3 * t^4 ) but then still
A* (μIR*R/2) * 3/( z^3*t )

6. Nov 24, 2007

### captain.joco

Is this anywhere near to correct?

7. Nov 24, 2007

### G01

I think you are missing a minus sign in there. You should have picked up a -3 with the differentiation.

Other than that, it looks good.

8. Nov 25, 2007

### captain.joco

But from the original equation which is emf = - dΦ/dt, so this minus cancels out with the -3 minus.. I will redo it just in case. That's for all the help, you can count this one as solved ( I understood the main idea with the z being the only thing that changes with time! ). Thanks very much