2. (10 points) A hand-crank egg beater consists of two approximately rectangular

Question

2. (10 points) A hand-crank egg beater consists of two approximately rectangular metal loops each 8.0 by 4.0 cm in dimension which are attached to an axle and gear system. The gear system is attached to the crank which can be turned manually. The maximum speed a person can turn the crank is 180 revolutions per minute. The gear system multiplies this frequency by a factor of five so that the loops of the egg beater itself can turn at a maximum rate of 900 times per minute. If the beater is spun at this maximum rate in the Earth's magnetic field (0.000050 T) what is the peak value of the voltage that can be generated within one of the loops of the egg beater?

Explanation / Answer

E(emf) = N x B x w x A x sin (theta) where N = number of turns B = magnetic field (T) A = area of coil w = angular velocity (rad/s) theta = angle made by coil wrt perpendicular to the field

w=2*3.14*180/60

=6*3.14

=18.84rad/s

f=18.84/2*3.14

=3HZ

gear system multiply with frequency=5*3

=15Hz

E=5*10-5*18.84*32*10-4*sin90

=3014.4*10-9volts

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