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in Physics by (80.9k points)

An airplane has an aluminum antenna attached to its wing that extends 15 m from wingtip to wingtip. The plane is traveling north at 75 m/s in a region where Earth's magnetic field of 6.0 x 10-5 T is oriented as shown above.

a. On the figure below, indicate the direction of the magnetic force on electrons in the antenna. Justify your answer.

b. Determine the potential difference between the ends of the antenna.

c. The ends of the antenna are now connected by a conducting wire so that a closed circuit is formed as shown.

i. Describe the condition(s) that would be necessary for a current to be induced in the circuit. Give a specific example of how the condition(s) could be created.

ii. For the example you gave in i above, indicate the direction of the current in the antenna on the figure.

1 Answer

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Best answer

(a) Looking at the side view and then transferring back to the top view, we see that in the top view the magnetic field is basically pointing into the page. The component of the magnetic field we are concerned with actually does point directly into the page. Now using the LHR rule for the electrons they get pushed down, which is towards east.

(b) The emf is induced and given by ε = Blv . The perpendicular B is B sin θ as can be seen in the side view ε = B sin θ Lv = (6 x 10–5)(sin 55)(15)(75) = .055 V

(c) To induce a current, the flux needs to change. The earth magnetic field strength cannot be changed, but the component of that B field in the enclosed area can be altered which will change the flux and induce current flow. In order to do this, the plane could rise up, or down, or to sustain a current the plane could follow a wavelike pattern.

Or the plane could rock its wings back and forth. However, simply turning left or right would not work.

Direction: Let’s say the plane rises up, this will increase the component of the B field in the loop so current will flow to reduce this increased downward field in the loop. Current flows CCW to create and upwards field to cancel out the increased downwards B field based on Lenz Law.

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