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 μTμT and the dip angle is 56∘∘. You then put the turtles in a 1.3 mm 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 250-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 degrees ?

Answer 1

Earth’s magnetic field at the given location, Be = 50 μT

Dip at the location, α = 56⁰

Radius of the coil, r= 1.3 /2 = 0.65 mm = 0.65 x 10^-3 m

Number of turns in the coil, n = 250

The dip angle of net magnetic field, θ = 62⁰

Angle between the net field and earth’s field, θ1 = 62 – 56 = 6⁰

If b is the magnetic field due to the current in the coil then

Tan θ1 = B sin (90-56)/(Be + B Cos ( 90 – 56 ))

0.105 = 0.559 B/( Be + 0.829B)

Solving we get, B = 11.12 μT

Magnetic field at the centre of a coil, B = μ₀ nI/2r

11.12 x 10^-6 = 4 x 3.14 x 10^-7 x 250 x I/2 x 0.65 x 10^-3

Current in the coil, I = 1.86 x 10^-4 A