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 1.9 m diameter 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 100-turn horizontal coil wrapped around the tank. This creates a field that adds to that of the earth

PART A:

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

PART B:

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 ?

Explanation / Answer

(A) current will flow such that magnetic field due to current will be downward.

hence current will be in clockwise direction.

(B) Bx = 50uT cos56 = 27.96 uT

By = 50 uT sin56 = 41.45 uT

new field strength in vertical direction is Byf .

then tan62 = Byf / Bx

tan62 = Byf / 27.96

Byf = 52.6 uT

field due to current = 52.6 - 41.45 =11.14 uT

11.14 x 10^-5 = u0 I / (1.9)

( u0 = 4pi x 10^-7)

I = 168.4 A

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