# Homework Help: Magnetic field in the middle of the plate

1. Mar 31, 2012

### regisz90

1. The problem statement, all variables and given/known data
A charged plate (record) is rotating with frequency "f". What is the magnetic field generated in the middle of the record?

2. Relevant equations
f...frequency
Q...electric charge
B=?

3. The attempt at a solution
My idea was that the field in the middle is the sum of the elemental fields generated by the thin belts in distance r and thickness Δr with electric current I(r). But i dont know how to continue. Thanks for help.

2. Mar 31, 2012

### Uniquebum

I'd assume you need to use Biot-Savart's law and double integral to get it right.

3. Mar 31, 2012

### Staff: Mentor

Hi regisz90, Welcome to Physics Forums.

Your idea looks reasonable. Why don't you start by figuring out what the effective current would be for one of your thin belts at a given radius r from the center of the plate? Assume the belt has radius r and width dr. How much charge is contained in the belt?

4. Mar 31, 2012

### regisz90

I think the current is: I(r)=q(r)/T=q(r).f
where q(r) is the charge contained in belt, and q(r)=(Q*r*dr)/(R*R)
Is it right?

5. Mar 31, 2012

### Staff: Mentor

The expression for the current looks good, but I think that there's a factor of 2 missing from your expression for the charge.

6. Mar 31, 2012

### regisz90

yes, there is really a 2 factor. And how to continue?

7. Mar 31, 2012

### Staff: Mentor

What is the magnetic field at the center of a loop of current?

8. Mar 31, 2012

### regisz90

B(r)=(μ*I)/(2r) ? Im not sure

9. Mar 31, 2012

### Staff: Mentor

You should be able to look these things up in your notes, text, or via web search. Anyways, yes, that is the expression for the magnitude of the magnetic field produced at the center of a current loop.

So now you have a current and the magnetic field it produces for a single one of your "belts". What do you suppose the next step should be?

10. Mar 31, 2012

### regisz90

Put the expression for the current to the lasst expression for the magnetic field. Then integrate both sides?

11. Mar 31, 2012

### Staff: Mentor

Sounds like a plan What do you get?

12. Mar 31, 2012

### regisz90

B=(μ*Q*f)/R Is it the right solution?

13. Mar 31, 2012

### Staff: Mentor

Looks good to me.

14. Mar 31, 2012

thx for help