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A boy is playing with the empty rim of a cycle wheel of radius $40 \mathrm{~cm}$ by rolling it along a horizontal road towards north with angular speed of $20 \mathrm{rad} \mathrm{s}^{-1}$. Considering the effect of magnetic field of earth, the e.m.f induced in the rim is
(Horizontal component of earth's magnetic field $=0.26 \mathrm{G}$ )
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(Horizontal component of earth's magnetic field $=0.26 \mathrm{G}$ )
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The correct answer is:
Zero
Radius, $\mathrm{R}=40 \mathrm{~cm}=0.4 \mathrm{~m}$
Angular speed, $\omega=20 \mathrm{rad} / \mathrm{s}$
Horizontal component of Earth magnetic field
$\begin{aligned}
& \mathrm{B}_{\mathrm{H}}=0.26 \mathrm{G} \\
& =0.26 \times 10^{-4} \mathrm{~T} \\
& \mathrm{~B}=\mathrm{B}_{\mathrm{H}} \tan \delta \\
& \Rightarrow \mathrm{B}=\mathrm{B}_{\mathrm{H}}(0) \\
& \Rightarrow \mathrm{B}=0
\end{aligned}$
Hence, the magnetic field will not take part in production of emf.
$\therefore \mathrm{emf}=0$
Angular speed, $\omega=20 \mathrm{rad} / \mathrm{s}$
Horizontal component of Earth magnetic field
$\begin{aligned}
& \mathrm{B}_{\mathrm{H}}=0.26 \mathrm{G} \\
& =0.26 \times 10^{-4} \mathrm{~T} \\
& \mathrm{~B}=\mathrm{B}_{\mathrm{H}} \tan \delta \\
& \Rightarrow \mathrm{B}=\mathrm{B}_{\mathrm{H}}(0) \\
& \Rightarrow \mathrm{B}=0
\end{aligned}$
Hence, the magnetic field will not take part in production of emf.
$\therefore \mathrm{emf}=0$
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