Question:

A wheel with $20$ metallic spokes each $1\, m$ long is rotated with a speed of $120\, rpm$ in a plane perpendicular to a magnetic field of $0.4\, G$ . The induced emf between the axle and rim of the wheel will be, $(1 G = 10^{-4}\, T)$

Updated On: Jul 19, 2024

$2.51 \times 10^{-4}\,V$
$2.51 \times 10^{-5}\, V$
$4.0\times 10^{-5}\, V$
$2.51 \,V$

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The Correct Option is A

Solution and Explanation

\varepsilon=\frac{1}{2} B \omega r^{2}

\varepsilon=\frac{1}{2}\times\left(0.4\times10^{-4}\right)\times\left(2\pi\left[\frac{120}{60}\right]\right)\left(1\right)^{2}

\varepsilon=0.8\pi\times10^{-4}

\varepsilon=2.512\times10^{-4}

Volt

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Concepts Used:

Faradays Laws of Induction

There are two laws, given by Faraday which explain the phenomena of electromagnetic induction:

Faraday's First Law:

Whenever a conductor is placed in a varying magnetic field, an emf is induced. If the conductor circuit is closed, a current is induced, known as the induced current.

Faraday's Second Law:

The Emf induced inside a coil is equal to the rate of change of associated magnetic flux.

This law can be mathematically written as:

∈ $-N {\triangle \phi \over \triangle t}$

A wheel with 202020 metallic spokes each 1 m1\, m1m long is rotated with a speed of 120 rpm120\, rpm120rpm in a plane perpendicular to a magnetic field of 0.4 G0.4\, G0.4G. The induced emf between the axle and rim of the wheel will be, (1G=10−4 T)(1 G = 10^{-4}\, T)(1G=10−4T)