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 μT, but at any particular location it may be a bit more or less than this. A 1.00-mm-diameter current loop with 200 turns of wire is adjusted to carry a current of 0.199 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.
Required:
What is the strength of the earth's magnetic field at this location?

Answer 1

Answer:

50000 μT

Explanation:

From the given information:

the diameter of the loop = 1.0 mm = 0.001 m

no of turns (N) = 200

current (I) = 0.199 A

radius = d/2 = 0.001/2

= 5 × 10⁻⁴ m

Recall that;

the magnetic field at the centre of circular wire is:

$= \dfrac{\mu I N}{2R}$

$= \dfrac{4 \pi \times 10^{-7} \times 200 \times0.199}{2\times 5\times 10^{-4}}$

= 0.05 T

= 50000 μT

Since the centre of the earth's magnetic field is given to be equal to the magnetic field produced by the wire, then:

the earth's magnetic field = 50000 μT