What is the current in the current loop?

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To determine the current in a current loop that cancels the Earth's magnetic field, it is essential to set the magnetic field produced by the loop equal in magnitude but opposite in direction to the Earth's field. The equation I = B2r/μ₀N is relevant for calculating the current, 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 discussion raises the point that if the fields are perfectly opposing, the net magnetic field at the center would be zero, suggesting that the current could be zero. However, if the current is adjusted to create a field that matches the Earth's field in magnitude and direction, a non-zero current is necessary. The conclusion emphasizes the need to balance the fields rather than cancel them entirely.
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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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