Question

A wheel with ten metallic spokes each 0.50 m long is rotated with a speed of 120 rev/min in a plane normal to the earth’s magnetic field at the place. If the magnitude of the field is 0.4 Gauss, the induced e.m.f. between the axle and the rim of the wheel is equal to
(a) 1.256 × 10⁻³ V(b) 6.28 × 10⁻⁴ V(c) 1.256 × 10⁻⁴ V(d) 6.28 × 10⁻⁵ V

Answer 1

Correct Answer : D: 6.28 × 10⁻⁵ V

Explanation :

Metallic length = 0.5m

Angular speed of wheel = 120 rev/min=120 rev/60= 2 rev/sec

Magnetic field is =0.4 guass=0.4 x 10 ⁻⁴ T

Area= A=πr²θ /2π

= r²θ/2

Induced EMF = dφ/dt = d(BA)/dt =[B r²/2]dθ/dt

=B r²ω/2

here ω= 2πv

E=2π x 2 x0.4 x 10 ⁻⁴ x (0.5) ²/2

=6.28 × 10⁻⁵ V