Magnetic field in the middle of the plate

[regisz90]

Homework Statement

A charged plate (record) is rotating with frequency "f". What is the magnetic field generated in the middle of the record?

Homework Equations

R...radius
f...frequency
Q...electric charge
B=?

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 don't know how to continue. Thanks for help.

 

[Uniquebum]

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

 

[gneill]

Homework Statement

A charged plate (record) is rotating with frequency "f". What is the magnetic field generated in the middle of the record?

Homework Equations

R...radius
f...frequency
Q...electric charge
B=?

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 don't know how to continue. Thanks for help.

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?

 

[regisz90]

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?

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?

 

[gneill]

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?

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

 

[regisz90]

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

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

 

[gneill]

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

 

[regisz90]

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

B(r)=(μ*I)/(2r) ? I am not sure

 

[gneill]

B(r)=(μ*I)/(2r) ? I am not sure

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?

 

[regisz90]

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?

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

 

[gneill]

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

Sounds like a plan What do you get?

 

[regisz90]

Sounds like a plan What do you get?

B=(μ*Q*f)/R Is it the right solution?

 

[gneill]

B=(μ*Q*f)/R Is it the right solution?

Looks good to me.

 

[regisz90]

Looks good to me.

thx for help