For a particular scientific experiment, it is important to be completely isolate

Question

For a particular scientific experiment, it is important to be completely isolated from any magnetic field, including the earth's field. The earth's field is approximately 50 T, but at any particular location it may be a bit more or less than this. A 1.00-m-diameter current loop with 200 turns of wire is adjusted to carry a current of 0.203 A ; at this current, the coil's field at the center is exactly equal to the earth's field in magnitude but opposite in direction, so that the total field at the center of the coil is zero.

What is the strength of the earth's magnetic field at this location?

Explanation / Answer

The axial magnetic field due to N current loops and radius R is:
B = I N / (2R)

Where:
= 4 x 10E-7
I = current (A) = 0.203
R = radius = 0.5 m
N = number of turns = 200 turns
B = magnetic field strength =...?

Now,
B = I N / (2R)
Hence:
4 x 10E-7 * 0.203* *200 / ( 2*1.00)

= 2.5 E-7

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