One method of magnetic braking is illustrated in this problem. The sketch at the

Question

One method of magnetic braking is illustrated in this problem. The sketch at the right shows a rod sliding on frictionless rails. The B-field is directed out of the page; its magnitude is B. The rails have total resistance R and are separated by distance L.

a) When the rod has speed v then what is the braking force? (Does the direction of velocity matter?)

b) If the mass of the rod is m then write the equation for acceleration (= dv/dt).

c) If the initial speed is Vo then how far does the rod travel?

Explanation / Answer

The flux between the resistor and bar is given by ?cos)(txBB??=F where x(t) is the distance of the bar from the top of the rails. Then, ??ecos)(cos)(tvBtxBdtddtdB????-=-=F-= Because the resistance of the circuit is R, the magnitude of the induced current is RtvBRI?ecos)(??== By Lenz’s law, the induced current produces magnetic fields which tend to oppose the change in magnetic flux. Therefore, the current flows clockwise, from b to a across the (b) At terminal velocity, the net force along the rail is zero, that is gravity is balanced by the magnetic force:

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