At the equator, the earth’s field is essentially horizontal; near the north pole

Question

At the equator, the earth’s field is essentially horizontal; near the north pole, it is nearly vertical. In between, the angle varies. As you move farther north, the dip angle, the angle of the earth’s field below horizontal, steadily increases. Green turtles seem to use this dip angle to determine their latitude. Suppose you are a researcher wanting to test this idea. You have gathered green turtle hatchlings from a beach where the magnetic field strength is 50 T and the dip angle is 56 . You then put the turtles in a 1.0 mdiameter circular tank and monitor the direction in which they swim as you vary the magnetic field in the tank. You change the field by passing a current through a 50-turn horizontal coil wrapped around the tank. This creates a field that adds to that of the earth.

What current should you pass through the coil, to produce a net field in the center of the tank that has a dip angle of 62 ?

Answer is not .043 or .0043

Explanation / Answer

The vertical component of the earth’s field is
B(earth)y = - 50 * 10-6T x sin62 = -4.41 * 10-5
The field of the coil must have the same magnitude at the center. The 2R in the equation is just the
diameter of the coil, 1 m. Thus

Bcoil = m0NI/2R = 4.41 * 10-5

I = 4.41 * 10-5 x 2R / u0N

= 4.41 * 10-5 x 2 x 1 / (1.26 * 10-6 x 50)

= 1.4A

Please review the calculations however the approach is correct

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