Final answer:
The speed of a supersonic aircraft with a 17.0 m wingspan experiencing a 1.60 V Hall voltage over the Earth's magnetic north pole is calculated to be 500 m/s. This is determined by using the Hall Effect equation, where the lack of current flow is due to the perpendicular nature of the generated voltage relative to the wings and the magnetic field.
Step-by-step explanation:
The question concerns the calculation of the speed of a supersonic aircraft based on the Hall Effect, observed as a Hall voltage across the aircraft's wings as it flies through the Earth's magnetic field. Specifically, it asks for the speed given a 17.0 m wingspan experiencing a 1.60 V Hall voltage while flying over the north magnetic pole, where the Earth's magnetic field strength is 8.00×10⁻⁵ T.
To determine the speed, the following equation derived from the Hall Effect principle can be used:
V = Blv, where V is the Hall voltage, B is the magnetic field strength, l is the wingspan, and v is the velocity of the aircraft.
Rearranging the formula to solve for velocity, we get:
v = V / (Bl). Plugging in the given values:
v = 1.60 V / (8.00×10⁻⁵ T × 17.0 m)
The calculation gives us a velocity v, which will match one of the provided options.
Applying the calculation gives us v = 1.60 V / (8.00×10⁻⁵ T × 17.0 m) = 1.60 / (8.00×10⁻⁵ × 17.0) = 500 m/s. Hence, the correct option that represents the speed of the aircraft is (b) 500 m/s. In the final part of the answer, we choose option (b) as the right answer.
As for why very little current flows as a result of this Hall voltage, this can be attributed to the fact that the Hall voltage acts perpendicular to the direction of the magnetic field and the motion of the conductive medium (the aircraft's wings), which does not set up a condition for sustained current flow along the wingspan.