PhysicsBowl 2018 Q35

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PhysicsBowl 2018

35) This question asks us to find the average electromotive force induced by the change in magnetic field. The relation between these is established with Faraday's Law.

Where Ɛ is electromotive force, N is the number of turns, Φ is the magnetic flux, and t is time

Faraday's law defines that the induced voltage through one loop of wire, is the quotient of the change in magnetic flux and the change in time. Since we just need the average emf, using the change over a time interval will be fine.

It is important to know that the negative sign should not be included in the answer, but it there to signify Lenz's law, which states that the direction of the electromagnetic force will oppose the change in flux.

Flux is a measure of the total electric field passing through an area.

Where Φ is the magnetic flux, E is magnetic field, A is the area of the loop, and θ is the measure of the angle the direction of the field makes with the normal to the surface

Keep in mind that the problem specifies that the magnetic field acts perpendicular to the plane, which means it is in the same direction as the normal line of the surface. Therefore, θ will be 0 and cos(0) = 1.

Finally, let's plug in the necessary values to solve this problem.

Where Ɛ is electromotive force, N is the number of turns, Φ is the magnetic flux, t is time, E is magnetic field, A is area of loop, and θ is the measure of the angle the direction of the field makes with the normal to the surface

Answer: D