What is the current in the current loop?

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SUMMARY

The discussion centers on calculating the current in a 1.00m diameter current loop with 200 turns of wire, designed to create a magnetic field that opposes the Earth's magnetic field. The relevant equation used is I = B2r/μ₀N, where B represents the magnetic field strength, r is the radius, μ₀ is the permeability of free space, and N is the number of turns. The key point of contention is whether to set the magnetic field B to zero due to cancellation with the Earth's field or to calculate the current directly using the opposing field concept. The correct approach involves ensuring the coil's magnetic field matches the Earth's field in magnitude but opposes it, thus requiring a non-zero current.

PREREQUISITES
  • Understanding of magnetic fields and their interactions
  • Familiarity with Ampère's Law and magnetic field equations
  • Knowledge of the permeability of free space (μ₀)
  • Basic principles of electromagnetism and current loops
NEXT STEPS
  • Study the derivation and applications of Ampère's Law
  • Learn about the concept of magnetic field cancellation in current loops
  • Explore the properties of the permeability of free space (μ₀)
  • Investigate the effects of varying current on magnetic field strength in loops
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Physics students, electrical engineers, and anyone interested in electromagnetism and magnetic field calculations.

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Homework Statement


It is important to be completely isolated from any magnetic field, including the Earth's field. A 1.00m diameter current loop with 200 turns of wire is set up so that the field at the center is exactly equal to the Earth's field in magnitude but opposite in direction. What is the current in the current loop?


Homework Equations


I=B2r/mew(naught)


The Attempt at a Solution


The part of the question that states "wire is set up so that the field at the center is exactly equal to the Earth's field in magnitude but opposite in direction" makes me think that we set B=0 rather than using the Earth's magnetic field because opposing fields cancel. If this the the case the current would be zero correct?

If this is not the case then the question is trivial (just plug and chug).

Which way is correct?
 
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B = μο*N*I/2r.
Set the coil such that the plane of the coil is in east-west direction. Set the magnitude and the direction of the current in the coil such that the field at the center is equal B(E) and direction is towards south.
 

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