17-8 AC Generator Due in 3 hours, 48 minutes A conducting rod of length 19 cm li

Question

17-8 AC Generator Due in 3 hours, 48 minutes A conducting rod of length 19 cm lies parallel to the y axis and moves in the x direction with a displacement given by x(t)-2.47 cos(287 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 2.9 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 jlow in the ty direction in the bar. Enter your answer as a formula. As an example, the original unction would be entered as 2·47scos ( 287 t ) where you should notice that each multiplication has to be shown explicity

Explanation / Answer

x(t) = 2.47 Cos(287 t) cm = 0.0247 Cos(287 t) m

velocity is given as

v(t) = dx(t)/dt = (0.0247) (287) (- Sin(287 t)) = - 7.1 Sin(287 t) i

B = magnetic field = 2.9 k

motional emf is given as

E = BL v = (2.9) (0.19) (7.1 Sin(287 t))

E = 3.91 Sin(287 t)

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