It is known that birds can detect the earth's magnetic field, but the mechanism of how they do this is not known. It has been suggested that perhaps they detect a motional EMF as they fly north to south, but it turns out that the induced voltages are small compared to the voltages normally encountered in cells, so this is probably not the mechanism involved. To check this out, calculate the induced voltage for a wild goose with a wingspan of 1.2 m flying due south at 13 m/s at a point where the earth's magnetic field is 5 x 10-5 T directed downward from horizontal by 40-degrees. The expected voltage would be about:A) .50 mV B) .25 mV C) .60 mV D) .060 mV E) .78 mV

In this problem, we can think the wings of the bird as a metal rod moving across a magnetic field. So, and emf will be induced into the wings of the bird, according to the formula:

[tex]\epsilon = BvL sin \theta[/tex]

where

[tex]B=5\cdot 10^{-5} T[/tex] is the strength of the magnetic field

v = 13 m/s is the speed of the bird

L = 1.2 m is the wingspan of the bird

[tex]\theta=40^{\circ}[/tex] is the angle between the direction of motion and the direction of the magnetic field

Substituting numbers into the formula, we find

[tex]\epsilon = (5.0\cdot 10^{-5} T)(13 m/s)(1.2 m) sin 40^{\circ}=0.00050 V = 0.50 mV[/tex]