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 μT and the dip angle is 56∘. 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 100-turn horizontal coil wrapped around the tank. This creates a field that adds to that of the earth.

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∘ ? [ANSWER: CLOCKWISE]
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∘ ?

Please show step-by-step solution. Thank you!

Answer 1

a) so as the magnetic field at a perticular dip angle is given by

so as dip angle increases magnetic field increase

so at 62 degree magnetic field wpould be greater than 56 degree

so in order to increse magnetic field in net direction current has to flow in clockwie diection so that net magnetic field is equal to which is at 62 degree

so,

2) magnetic field at 56 degree is given so

so,

so,

net magnetic field in 62 degrre than

so net change iin magnetic field is

now magnetic field due to loop

so,

plug in values we get current