Question

Bats can navigate using the earth’s field—a plus for an animal that may fly great distances from its roost at night. If, while sleeping during the day, bats are exposed to a field of a similar magnitude but different direction than the earth’s field, they are more likely to lose their way during their next lengthy night flight. Suppose you are a researcher doing such an experiment in a location where the earth’s field is 52 µT at a 60° angle below horizontal. You make a 50-cm-diameter, 100-turn coil around a roosting box; the sleeping bats are at the center of the coil.

a) Draw a diagram of the field and compute the magnitude of the horizontal and vertical components. The horizontal component points north.

b) If you add a horizontal field that is double the earth’s horizontal field but that points south, what is the new horizontal component?

c) Describe the magnitude and direction of the total field. How might you expect this to affect the bat’s navigation?

d) What current do you need in the coil to produce the noted field? What is the necessary orientation of the axis of the coil?

Answer 1

a)

The horizontal component, whic points north is

The vertical component, which points downward is

b) We add horizontal component of 52 micro Telsa that points towards South. If we consider North direction as positive X axis then, this field points along negative X-axis. From the vector sum, we get total field as

Thus, new horizontal component is 26 micro Tesla, which points towards South.

c) Due to new field, the magnitude of the new field, which has component of 26 micro Tesla towards South and 45 micro Tesla downward, is

The angle the resultant field makes with the downward direction is

So, the total field points at 60 degrees with the South.

This, will drive the bat in the opposite direction of navigation, as the field at 60 degrees but in the opposite direction.

d) For a current carrying coil of N turns, the magnetic field at the center is given by

The coil must be along South-North direction.