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  • 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

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 \mathrm{H}=0.4 \times 10^{-4} \mathrm{~T} at the place, then induced emf between the axle and the rim of the wheel is:

Option: 1

\mathrm{2.3 \times 10^{-4} \mathrm{~V}}


Option: 2

\mathrm{3.1 \times 10^{-4} \mathrm{~V}}


Option: 3

\mathrm{2.9 \times 10^{-4} \mathrm{~V}}


Option: 4

\mathrm{1.61 \times 10^{-4} \mathrm{~V}}


Answers (1)

best_answer

Here , \mathrm{H}=\mathrm{B}=0.4 \times 10^{-4} \mathrm{~T}, l=0.8 \mathrm{~m}, \mathrm{v}=120 \mathrm{rpm}=2 \mathrm{rps}

Emf induced across the ends of each spoke

\mathrm{\begin{aligned} & \varepsilon=\frac{1}{2} \mathrm{~B} \omega l^2=\frac{1}{2} \mathrm{~B}(2 \pi \mathrm{v}) l^2 \\ & =\mathrm{B} \pi \mathrm{v} l^2 \\ & \therefore \quad \varepsilon=0.4 \times 10^{-4} \times \pi \times 2 \times(0.8)^2=1.61 \times 10^{-4} \mathrm{~V} \end{aligned}}

 

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Ritika Jonwal

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