Lenz's Law

Question

An airplane travelling at 278 m/s upward at an angle of 30 o to the horizontal is in a region where earth's magnetic field is 5.0 x 10-5 T upward (vertical field from the ground to the sky). What is the potential difference induced between the wing tips that are 80 m apart? 

Answer 1

This is actually a problem of induced emf, not Lenz's law.  The airplane (assumed to be made of metal) is a conductor moving through a magnetic field.  An emf will be induced along the length of the conductor.

 

v = speed of the moving conductor = 278 m/s, 30° above the local horizontal

B = magnetic field of strength = 5.0 x 10^-5 T, pointing vertically upward from the surface of the earth

θ = angle between the direction the conductor is moving, and the direction of the magnetic field

θ = 90° - 30° = 60° 

L = length of the conductor = 80 m (wing tip to wing tip)

E = induced emf = ?

 

You probably saw in your physics class the formula

 

E = -BLv sinθ

 

(The minus sign comes from Lenz's law.)

 

E = -(5.0 x 10^-5 T)(80 m)(278 m/s)(sin60°) ≅ -0.963 volts

 

The induced emf is the potential difference that you seek.