2.1 Falling Loop: A rectangular loop is w in width and very long in height. It i

Question

2.1 Falling Loop:

A rectangular loop is w in width and very long in height. It is held vertical, initially at rest. The loop has internal resistance R. It is in a region of space where there is a uniform magnetic field of strength B0 which is perpendicular to the plane of the loop. The region of space directly below the loop has no magnetic field in it. When the loop is dropped the magnetic flux will change and the loop will experience an induced EMF, and an induced current. Obtain an expression for the vertical force on the top edge as a result of the induced current and the externally applied field.

Explanation / Answer

Note that

emf = B w v

As it is falling,

v = gt

Thus,

emf = B w g t

Thus, the current flowing is

I = emf / R

I = B w g t / R

As the force on a current is

F = B I w

Then

F = B^2 w^2 g t / R   [ANSWER]

where t is time, g = 9.8 m/s^2.

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