Magnetic field in the middle of the plate

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Homework Help Overview

The problem involves a charged rotating plate, referred to as a record, and seeks to determine the magnetic field generated at its center based on its frequency of rotation.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the use of Biot-Savart's law and the concept of summing elemental fields from thin belts of charge. There are inquiries about the effective current for these belts and the charge contained within them. Some participants question the correctness of expressions related to current and charge.

Discussion Status

There is an ongoing exploration of the relationships between current, charge, and magnetic field. Participants are providing guidance on how to approach the problem, with suggestions to integrate expressions and check for missing factors in calculations. Multiple interpretations of the problem setup are being considered.

Contextual Notes

Participants are working under the constraints of homework rules, which may limit the amount of direct assistance provided. There is a focus on ensuring that assumptions about charge distribution and current are critically examined.

regisz90
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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.
 
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I'd assume you need to use Biot-Savart's law and double integral to get it right.
 
regisz90 said:

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?
 
gneill said:
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?
 
regisz90 said:
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.
 
gneill said:
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?
 
What is the magnetic field at the center of a loop of current?
 
gneill said:
What is the magnetic field at the center of a loop of current?

B(r)=(μ*I)/(2r) ? I am not sure
 
regisz90 said:
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?
 
  • #10
gneill said:
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?
 
  • #11
regisz90 said:
Put the expression for the current to the lasst expression for the magnetic field. Then integrate both sides?

Sounds like a plan :wink: What do you get?
 
  • #12
gneill said:
Sounds like a plan :wink: What do you get?

B=(μ*Q*f)/R Is it the right solution?
 
  • #13
regisz90 said:
B=(μ*Q*f)/R Is it the right solution?

Looks good to me.
 
  • #14
gneill said:
Looks good to me.

thx for help
 

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