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 mu T and the dip angle is 56 degree. You then put the turtles in a 2.0 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 50-tum horizontal coil wrapped around the tank. This creates a field that adds to that of the earth. 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 degree ? 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 degree ? Express your answer to two significant figures and include the appropriate units.

Respuesta :

Answer:

Direction of current = clockwise

Magnitude of current, I = 0.36 A

Explanation:

The magnetic field strength, [tex]B_{E} = 50 \mu T[/tex]

The angle of dip, ∅ = 56°

The net magnetic field in the center of the tank is:

[tex]B_{net} = (B_{E} cos \phi ) (\hat{x} ) + ( B + B_{E} sin \phi)(-\hat{y})\\B_{net} = (50 cos 56 ) (\hat{x} ) + ( B +50 sin 56)(-\hat{y})\\B_{net} = (28 \mu T ) (\hat{x} ) + ( B +41.4 \mu T)(-\hat{y})\\[/tex]

The direction of the net magnetic field is:

[tex]\phi = tan^{-1} \frac{B + 41.4 }{28} \\tan \phi = \frac{B + 41.4 }{28}\\\phi = 62^0\\tan 62 = \frac{B + 41.4 }{28}\\28 tan 62 = B + 41.4\\52.66 = B + 41.4\\B = 11.26 \mu T[/tex]

The magnetic field due to the coil:

[tex]B = \frac{\mu_{0}NI }{2r} \\11.26 * 10^{-6} = \frac{4\pi * 10^{-7} * 50 *I }{2 *1}\\I = \frac{2 * 11.26 * 10^{-6}}{4\pi * 10^{-7} * 50} \\I = 0.36 A[/tex]

The current must be in clockwise direction to produce the field in downward direction

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