Rotating Coil in Magnetic Field

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SUMMARY

The discussion focuses on calculating the magnetic field (B) using a search coil method, specifically a 61-turn coil with a resistance of 194Ω and a cross-sectional area of 44.5m². The total charge of 4.76E-4C is measured as the coil rotates from a perpendicular to a parallel position relative to the magnetic field. Key equations include Faraday's law of electromagnetic induction, which relates emf to the change in magnetic flux, and the relationship between charge, current, and resistance. The participants emphasize the importance of integrating these concepts to derive the correct relationship between total charge and magnetic flux change.

PREREQUISITES
  • Understanding of Faraday's law of electromagnetic induction
  • Knowledge of the relationship between charge, current, and time
  • Familiarity with Ohm's law (emf = current * resistance)
  • Basic concepts of magnetic flux and coil geometry
NEXT STEPS
  • Study the derivation of Faraday's law and its applications in electromagnetic induction
  • Learn how to calculate magnetic flux for different coil configurations
  • Explore the relationship between charge, current, and resistance in electrical circuits
  • Investigate practical applications of search coils in measuring magnetic fields
USEFUL FOR

Physics students, electrical engineers, and anyone interested in the principles of electromagnetism and practical applications of magnetic field measurements.

dukesolice
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Homework Statement


[/B]
Magnetic field values are often determined by using a device known as a search coil. This technique depends on the measurement of the total charge passing through a coil in a time interval during which the magnetic flux linking the windings changes either because of the motion of the coil or because of a change in the value of B. As a specific example, calculate B when a 61-turn coil of resistance 194Ω and cross-sectional area 44.5m^2 produces the following results: A total charge of 4.76E-4C passes through the coil when it is rotated in a uniform field from a position where the plane of the coil is perpendicular to the field to a position where the coil's plane is parallel to the field.

Homework Equations


emf = -change in flux

The Attempt at a Solution



emf = -d/dt (integral of B dot dA)

The change in flux is from when the coil is perpendicular to the field to when the coil is parallel to the field. So 90 degrees. But I don't know how to get the change the in area, and how to use the charge and resistance.
 
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dukesolice said:
But I don't know how to get the change the in area, and how to use the charge and resistance.
The shape of the coil doesn't change as the coil rotates. So, the area of the coil remains constant.

You'll need to bring together several elementary concepts in this problem. How is charge related to current and time? How is current related to resistance and emf?
 
TSny said:
The shape of the coil doesn't change as the coil rotates. So, the area of the coil remains constant.

You'll need to bring together several elementary concepts in this problem. How is charge related to current and time? How is current related to resistance and emf?

Current is charge/time. Emf = current * resistance.
 
dukesolice said:
Current is charge/time. Emf = current * resistance.
OK. These relations along with Faraday's law give you everything you need.

Try combining them to get a relation between the total charge and the change of flux.
 
dukesolice said:

Homework Equations


emf = -change in flux
This is not correct. Faraday's law also involves time.
 
So now I have dQ/dt * R = -d(flux)/dt, so then I took integral of both sides and got NRQ = -BA, where N is number of coils, this gave me the wrong answer
 
dukesolice said:
So now I have dQ/dt * R = -d(flux)/dt,
OK, but should the number of turns, N, appear somewhere here?

so then I took integral of both sides and got NRQ = -BA, where N is number of coils, this gave me the wrong answer
Show the steps in getting to this result. Why does N appear on the left?
 

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