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 1.0 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 200-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 ∘ ? Express your answer to two significant figures and include the appropriate units.

Answer 1

To produce a dip angle of 62° in the center of the tank, a current of 18.8 A should be passed through the coil.

Step-by-step explanation:

In order to produce a net magnetic field in the center of the tank with a dip angle of 62°, you will need to pass a current through the coil that creates a magnetic field that adds to the Earth's magnetic field. The change in magnetic field strength needed can be calculated using the tangent function:

Tan θ = B_coil / B_earth

Solving for B_coil and substituting the given dip angles, we have:

B_coil = Tan(dip angle) * B_earth = Tan(62°) * 50 μT = 1.19 mT

Using the formula for the magnetic field inside a current-carrying loop:

B_coil = (μ0 * I * N) / R

Where μ0 is the permeability of free space, I is the current through the coil, N is the number of turns in the coil, and R is the radius of the coil. Simplifying for I, we have:

I = (B_coil * R) / (μ0 * N) = (1.19 mT * 0.5 m) / (4π × 10^-7 T·m/A * 200) = 18.8 A

Therefore, you should pass a current of 18.8 A through the coil to produce a net magnetic field in the center of the tank with a dip angle of 62°.