Question

g Suppose you have this brilliant idea: A Ferris wheel has radial metallic spokes between the hub and the circular rim (of radius roughly 16 m). These spokes move in the magnetic field of the Earth (5e-05 T), so each spoke acts like a rotating bar in a magnetic field. The magnetic field points perpendicular to the plane of the Ferris wheel. You plan to use the emf generated by the rotation of the Ferris wheel to power the light-bulbs on the wheel. Suppose the period of rotation for the Ferris wheel is 90 seconds. What is the magnitude of the induced emf between the hub and the rim

Answer 1

Answer:

$4.46\times 10^{-4}\ \text{V}$

Explanation:

B = Magnetic field = $5\times 10^{-5}\ \text{T}$

r = Radius of rim = 16 m

t = Time = 90 seconds

A = Area of rim = $\pi r^2$

EMF is given by

$\varepsilon=\dfrac{BA}{t}\\\Rightarrow \varepsilon=\dfrac{5\times 10^{-5}\times \pi\times 16^2}{90}\\\Rightarrow \varepsilon=0.000446=4.46\times 10^{-4}\ \text{V}$

The magnitude of the induced emf between the hub and the rim is $4.46\times 10^{-4}\ \text{V}$.