A bicycle is resting on its stand in the east-west direction and the rear wheel is rotated at an angular speed of 100 revolutions per minute. If the length of each spoke is 30.0 cm and the horizontal component of the earth’s magnetic field is 2.0 × 10 –5 T, find the emf induced between the axis and the outer end of a spoke. Neglect centripetal force acting on the free electrons of the spoke.

Question

Philoid · Accepted Answer

Given:

Angular speed(w) = 100 revolutions/minute x 2π = 100 revolutions/60 sec x 2π= 10π/3 revolutions/sec

Length of each spoke(l) = 30 cm = 0.3 m

Magnetic field(B) = 2.0 × 10^–5 T

Formula used:

Induced emf … (i), where B = magnetic field, l = length of spoke, v = velocity

Now, linear speed of the spoke v = ωr, where ω = angular speed, r = distance from the axis to the outer end.

Here, , where l = length of spoke

Hence,

Therefore, emf induced (from (i))

⇒ V = 9.42 x 10^-6 V (Ans)