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?

Solution

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

Required

Induced emf, ε =?

Formula

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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