Question

A wheel with $20$ metallic spokes each of length $0.8m$ long is rotated with a speed of $120$ revolution per minute in a plane normal to the horizontal component of earth magnetic field $H$ at a place. If $H=0.4\times 10^{-4}T$ at the place, then induced emf between the axle and the rim of the wheel is

• A. $2.3\times 10^{-4}V$
• B. $3.1\times 10^{-4}V$
• C. $2.9\times 10^{-4}V$
• D. $1.61\times 10^{-4}V$

Answer 1

Answer: (D)

Here, $H=B=0.4\times 10^{-4}T$,
$l=0.8m$
$\upsilon =120rpm=2rps$
Emf induced across the ends of each spoke
$\epsilon =\frac{1}{2}B\omega l^2=\frac{1}{2}B\left(2\pi \upsilon \right)l^2\left(\because \omega =2\pi \upsilon \right)$
$=B\pi \upsilon l^2$
$\therefore \epsilon =0.4\times 10^{-4}\times \pi \times 2\times {\left(0.8\right)}^2$
$=1.61\times 10^{-4}V$