# Metal Detector Coils

1. Nov 22, 2006

### Sir_Pogo

Can i get some help with this problem?
This problem deals with the basic loop configuration you will use in the laboratory to construct a metal detector. Two concentric circular coils of wire lie in a plane. The larger coil has 49 turns and a radius of a = 7.90 cm. The smaller coil also has 49 turns but has a radius of b = 0.85 cm. The current in the larger coil has a time dependence given by = Io sin(ωt) where ω = 14,000 rad/s and Io = 0.50 A. What is the magnitude of the EMF induced in the small coil at t = 2.00 s if you make the approximation that the magnetic field inside the small coil is spatially uniform?

2. Nov 22, 2006

### OlderDan

Show us some attempt to solve the problem. What do you know that you think is relevant to the solution?

3. Nov 23, 2006

### Sir_Pogo

Are there any hints on this one...I am using Faraday's Law
where EMF = N*(change in flux over change in time). The
magnetic flux is equal to BA, which is the B for the center
of a loop (with radius of the outer circle) times A for the
inner circle...my final equation is coming out something
like this...[(N^2)*Pi*Rb^2*mu*I(nought)*w*cos(w*t)]/(2*Ra)

This is long, but it seems right to me...Any suggestions?

4. Nov 23, 2006

### Sir_Pogo

the velocity induces an emf, the emf gives a current, and
the current gives a backward force F=ILB, so you can set up
and equation mdv/dt=F=-Cv, for some const C you will get.
am i right? im still not getting the right answer

5. Nov 24, 2006

### OlderDan

This looks OK, although the answer might be looking for a minus because the emf is the negative of the flux derivative.

6. Nov 24, 2006

### OlderDan

I assume this was supposed to go with your other problem. It is right if you get C right. So as it asks in the other thread, what function for v will give you a derivative proportional to v?

7. Nov 24, 2008

### aamybush

I have tried to solved it and got answer in minus more then one time so its might possible. I think you are right...

8. Dec 1, 2008

### aamybush

Last edited by a moderator: Apr 24, 2017