A conducting rod of length 17 cm lies parallel to the y axis and moves in the x

Question

A conducting rod of length 17 cm lies parallel to the y axis and moves in the x direction with a displacement given by x(t) = 3.79 cos (557 t) cm, where t is in seconds to make the argument of the trig function come out in radians. The rod is in a uniform magnetic field of 2.8 T that is in the +z direction. What is the EMF induced in the rod as a function of time? Use a standard sign convention where the EMF is positive when it would make a current flow in the +y direction in the bar. Enter your answer as a formula. As an example, the original function would be entered as 3.7 9*cos (557*t) where you should notice that each multiplication has to be shown explicitly. V(t) = V

Explanation / Answer

induced emf =B * (dx/dt) * l

x(t) = 3.79 cos(557 t) cm,

dx/dt =-3.79 * sin(557t) * 557 =-2111.03cm/s sin(557) = -21.1103 sin(557t) m/s

induced emf =B * (dx/dt) x l =2.8T x -21.1103 sin(557t) m/s x 0.17m = -10.048 sin(557t)

v(t) = 10.048V

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