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

Given:-

Length of the spoke of the bicycle's wheel, l = 0.3 m

Earth's magnetic field,

\[\overrightarrow B=2.0\times10^{-5}T\]

Length of each spoke = 30.0 cm = 0.3 m

Angular speed of the wheel,

\[\omega = \frac{100}{60} \times 2\pi = \frac{10}{3}\pi  rad/s\]

Linear speed of the spoke,

\[v = \frac{l}{2} \times \omega = \frac{0 . 3}{2} \times \frac{10}{3}\pi\]

Now,

Emf induced in the spoke of the wheel, e = Blv

\[\Rightarrow e = (2 . 0 \times {10}^{- 5} ) \times (0 . 3) \times \left( \frac{0 . 3}{2} \times \frac{10}{3} \times \pi \right)\]

= 3π × 10⁻⁶ V

= 3 × 3.14 × 10⁻⁶V

= 9.42 × 10⁻⁶ V