Question

A wheel with $20$ metallic spokes, each $0.5\text{m}$ long, is rotated with a speed of 4 rev/s in a plane normal to horizontal component of earth's magnetic field $B_H=0.5\text{G}$. What is emf induced between axle and rim of the wheel?

• A. $1.57\times {10}^{-4}\text{V}$
• B. $3.14\times {10}^{-3}\text{V}$
• C. $7.85\times {10}^{-4}\text{V}$
• D. $6.28\times {10}^{-3}\text{V}$

Answer 1

The correct option is A $1.57\times {10}^{-4}\text{V}$

Induced emf between axel and rim, $\epsilon =\frac{1}{2}B{R}^2\omega$
$\epsilon =\frac{1}{2}\times 0.5\times {10}^{-4}\times {\left(\frac{1}{2}\right)}^2\times 2\pi \times \left(4\right)$
$\epsilon =\frac{1}{2}\times \frac{1}{2}\times \frac{1}{4}\times 2\pi \times 4\times {10}^{-4}=\frac{\pi }{2}\times {10}^{-4}$
$\epsilon =1.57\times {10}^{-4}\text{V}$