Explaining motional emf in terms of the hall effect?

[ice109]

im thinking of the classic airplane problem. the one where the flying airplane develops a voltage across its wingspan. now this was posed to me as a motional emf problem and i bought it then but simultaneously thought that it seemed like a hall effect problem.

so two questions

now that i think back. how is this a motional emf problem?there's no current loop? the only way i could see it as that if you thought of the wingspan as an antenna that developed a voltage across simply because of E field that is concomitant to the Earth's B field. but how is there a $$\frac{d\phi}{dt}$$?

and
how can i solve a problem like this as a hall effect problem?

i can't find one right now but any random numbers would do

airplane flying 30m/s and having a 30m wingspan.

edit

this is not a homework problem, the numbers are simply to serve as an example

 

[ice109]

anyone anyone?

 

[charng]

Motional emf and the Hall effect are two different phenomena that can both occur in the situation of an airplane flying through the Earth's magnetic field. Motional emf is the induced voltage that occurs in a conductor when it moves through a magnetic field, while the Hall effect is the generation of a voltage perpendicular to both the current and magnetic field in a conductive material.

In the case of the airplane, the motional emf is caused by the movement of the airplane through the Earth's magnetic field. This creates a changing magnetic flux through the wingspan of the airplane, which induces a voltage across the wingspan. This voltage is proportional to the speed of the airplane and the strength of the Earth's magnetic field.

On the other hand, the Hall effect is not directly involved in this situation. The Hall effect requires a current to be flowing in the conductor, which then experiences a force due to the interaction with the magnetic field. In the case of the airplane, there is no current flowing through the wingspan, so the Hall effect is not applicable.

To solve a problem like this as a Hall effect problem, you would need to have a current flowing through the wingspan of the airplane. This could be achieved by having a conducting wire connecting the two wings, or by having a current-carrying circuit on board the airplane. The voltage induced by the Hall effect would then be perpendicular to both the current and the magnetic field, and its magnitude would depend on the strength of the magnetic field and the current flowing in the wingspan.

In conclusion, the situation of an airplane flying through the Earth's magnetic field can be explained by motional emf, but not by the Hall effect. To solve this as a Hall effect problem, you would need to introduce a current in the wingspan of the airplane.