Falling loops. A long rectangular wire loop with mass m and resistance R is fall

Question

Falling loops. A long rectangular wire loop with mass m and resistance R is falling out of a region with a magnetic field with magnitude B_0 that is pointing out of the plane of the paper. The rectangle has a width w and a length that is so large that part of the loop is inside the region with the magnetic field and part is outside that region: (a) Determine the current in the wire when the rectangle is falling from the magnetic field with a speed nu. (b) When dropped from rest the speed of the loop increases from 0 up to the terminal velocity, and then remains constant at this terminal velocity. Determine the terminal velocity for the falling loop. (Assume that the terminal velocity is reached before the top of the loop leaves the magnetic field.)

Explanation / Answer

a)

since flux is changing EMF is induced

and the value of induced EMF is

E = BVw

we know that

current

i = E/R

i = Bvw/R

b)

force due to magnetic field = mg

iwB = mg

B^2 w^2 v/R = mg

V = mgR/B^2w^2

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