Question

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.

Answer 1

EMF is $9.42 \times 10^-^6$ V

Explanation:

ℓ = $0.3m, vector B = 2.0\times 10^-^5\ T,\ \omega = 100 rpm$

v = $\frac {100}{60} \times 2\pi = \frac {10}{3} \pi rads^-^1$

v = $\frac {l}{2} \times \omega = \frac {0.3}{2} \times \frac {10}{\pi}$

Emf = e = Blv

= $2.0 \times 10^-^5 \times 0.3 \times \frac {0.33}{2} \times \frac {10}{3} \pi$

= $3\pi \times 10^-^6$ V  

= $3 \times 3.14 \times 10^-^6$ V  

= $9.42 \times 10^-^6$ V