Problem 2: A wheel with 12 metal spokes each 0.6 m long is rotated with a speed of 180 rpm in a plane normal to earth’s magnetic field at a place. If the magnitude of the field is 0.6 G, what is the magnitude of induced emf between the axle and rim of the wheel?
Length of the metallic spoke, r = 0.6 m
Angular speed of the wheel = ω = 180 rev/min = 3 rev/s = 3 × 2π = 6π rad/s
(Here 1 revolution = 2π radians).
Local magnetic field of the earth = B = 0.6 Gauss = 0.6 × 10-4 T
Induced emf, ε =?
A is the area of the angle traversed by the spoke, given by
Put this value of A and the formula to be used becomes,
Now put the values from the given data in this formula
The spokes make a system of parallel emfs, so the emf between the rim and axle is the same.