Question

A wheel with $20$ metallic spokes each of length $0.8 \,m $ 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, $H = B = 0.4\times10^{-4}T$,
$l=0.8\,m$
$\upsilon =120 rpm =2\, rps$
Emf induced across the ends of each spoke
$\varepsilon=\frac{1}{2}B\omega l^{2}=\frac{1}{2}B \left(2\pi\upsilon\right)l^{2} \left(\because\omega=2\pi\upsilon\right)$
$=B\pi\upsilon l^{2}$
$\therefore \varepsilon=0.4\times10^{-4}\times\pi\times2\times\left(0.8\right)^{2}$
$=1.61\times10^{-4}\,V$