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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?


Given Data

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 =?


(Since B is constant).

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.



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