Question:
A copper disc of radius $ 0.1 \,m $ is rotated about its centre with $ 20\, rev/s $ in a uniform magnetic field of $ 0.1\, T $ with its plane perpendicular to the field. The emf induced across the radius of the disc is:
A copper disc of radius $ 0.1 \,m $ is rotated about its centre with $ 20\, rev/s $ in a uniform magnetic field of $ 0.1\, T $ with its plane perpendicular to the field. The emf induced across the radius of the disc is:
Updated On: Jun 6, 2022
- $ \frac{\pi }{20}V $
- $ \frac{\pi }{10}V $
- $ 20\pi \,mV $
- $ 10\pi \,mV $
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The Correct Option is C
Solution and Explanation
From Faradays law of electromagnetic induction
$ e=-\frac{d\phi }{dt}=-BAN. $
Given, $ B=0.1\text{ }T,\text{ }N=20,\text{ }A=\pi {{r}^{2}}=\pi {{(0.1)}^{2}}. $ $ \therefore $ $ e=-0.1\times 20\times \pi {{(0.1)}^{2}}=20\,\pi \,mV $
$ e=-\frac{d\phi }{dt}=-BAN. $
Given, $ B=0.1\text{ }T,\text{ }N=20,\text{ }A=\pi {{r}^{2}}=\pi {{(0.1)}^{2}}. $ $ \therefore $ $ e=-0.1\times 20\times \pi {{(0.1)}^{2}}=20\,\pi \,mV $
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Concepts Used:
Electromagnetic Induction
Electromagnetic Induction is a current produced by the voltage production due to a changing magnetic field. This happens in one of the two conditions:-
- When we place the conductor in a changing magnetic field.
- When the conductor constantly moves in a stationary field.
Formula:
The electromagnetic induction is mathematically represented as:-
e=N × d∅.dt
Where
- e = induced voltage
- N = number of turns in the coil
- Φ = Magnetic flux (This is the amount of magnetic field present on the surface)
- t = time
Applications of Electromagnetic Induction
- Electromagnetic induction in AC generator
- Electrical Transformers
- Magnetic Flow Meter