Question
Thu September 19, 2013 By: Krishna

# a wheel with 8 metallic spokes each 50cm long is rotated with a speed of 120rev/min in a plane normal to the horizontal component of the earths magnetic field .the earths magnetic field at the place is 0.4G and the angle of dip id 60degree .calculate the emf induced between the axle and the rim of the wheel.how will the value of emf be affected if the number of spokes were increased?

Sun September 22, 2013
first of all, the emf will be induced between the two ends of the spokes which are moving across the magnetic field. Thus emf will be across the rim and the axle. Hence increasing the no. of spokes wont effect the emf induced, it is acting like connecting a no. of cell parallel to each other.
Length of each spoke: L = 50 cm = 0.5 m
angular velocity, w = 120 rev/min
thus linear speed at a distance r from the center = w.r
for a length of segment of a spoke dr,
emf induced across it: d e = (B)(w.r)(dr)
here B can be calculated as direction of magnetic field perpendicular to the direction of rotation: B = 0.4 sin60

and now integrating d e from 0 to 0.5
we can get the emf
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