An inventor designs a model plane that uses the emf that develops across its metal wings as it flies through the earth's magnetic field to power the plane's propeller. Will this plane be able to power itself this way?

The plane will not be able to power itself this way because the induced emf will be very small and it cannot power the plane's propeller.

Explanation:

From Faraday's law, induced emf is directly proportional to the strength of the magnetic field and cross sectional area of the conductor.

emf = Earth's Magnetic field strength (B) x Cross sectional Area (A)

The magnitude of Earth's magnetic field strength is very small, with value ranging from 25μT to 65μT.

Thus, the emf that will develop across the plane metal wings as it flies through the earth's magnetic field will not power the plane's propeller.