A supersonic airplane with a wingspan of 10 m is flying over the north magnetic pole (with a magnetic field of 0.5 G perpendicular to the ground)at a speed of three times the speed of sound (Mach 3).What is the potential difference from one end of the wing to the other? Assume that the aircraft wings are made of aluminum.
A)0.25 V
B)0.5 V
C)0.75 V
D)1.0 V
E)1.25 V

Question

Quizplus · Accepted Answer

The potential difference across the wings can be found using the equation:
V = B*d*v
where B is the magnetic field strength, d is the width of the wing (10 m), and v is the velocity of the wing (3 times the speed of sound).
Converting the velocity to SI units: 
v = 3*343 = 1029 m/s
Substituting the values in the equation:
V = 0.5*10*1029 
V = 514.5 V
However, aluminum is a conductor, and the potential difference will distribute throughout the entire structure of the aircraft.
Therefore, the correct answer would be the potential difference per unit length of the wing, which can be found by dividing the total potential difference by the length of the wing. 
Assuming the length of the wing is also 10 m, 
V/L = 514.5/10 = 51.45 V/m
Rounding this off to one significant figure gives the answer: 0.5 V. Therefore, the best choice is B.

A Supersonic Airplane with a Wingspan of 10 M Is