(a) What is the speed of a supersonic aircraft with a wingspan, if it experiences a Hall voltage between its wing tips when in level flight over the north magnetic pole, where the Earth’s field strength is (b) Explain why very little current flows as a result of this Hall voltage.
(a) The speed of the aircraft is .
(b) The little number of current flows is a result of this Hall voltage as there exists a magnetic force pushing the charges in the opposite direction.
The wingspan of the supersonic aircraft is
The magnetic field strength of the earth is
Induced voltage due to the Hall effect is
An induced voltage generated by a charge carrier moving in an applied magnetic field perpendicular to the direction of motion can be expressed as,
Substitute the given data in equation (1) to evaluate the speed that produces such hall voltage can be given as,
Therefore the speed of supersonic aircraft is .
Very little current flows as a result of this Hall voltage due to the reason that there exists a magnetic force that pushes the charges in the opposite direction.
Therefore, the flow of a small current is due to the Hall voltage as there already exists a magnetic force pushing the charges in the opposite direction.
(a) Aircraft sometimes acquire small static charges. Suppose a supersonic jet has a charge and flies due west at a speed of 660 m/s over the Earth’s south magnetic pole, where the magnetic field points straight up. What are the direction and the magnitude of the magnetic force on the plane? (b) Discuss whether the value obtained in part (a) implies this is a significant or negligible effect.
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