Question:
A $10\, m$ long horizontal wire extends from North East to South West. It is falling with a speed of $5.0\,ms^{-1}$, at right angles to the horizontal component of the earth's magnetic field, of $0.3 \times 10^{-4}\,Wb/m^2$. The value of the induced emf in wire is :
A $10\, m$ long horizontal wire extends from North East to South West. It is falling with a speed of $5.0\,ms^{-1}$, at right angles to the horizontal component of the earth's magnetic field, of $0.3 \times 10^{-4}\,Wb/m^2$. The value of the induced emf in wire is :
Updated On: Sep 27, 2024
- $2.5 \times 10^{-3} V$
- $1.1 \times 10^{-3}V$
- $0.3 \times 10^{-3} V$
- $1.5 \times 10^{-3} V$
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The Correct Option is B
Solution and Explanation
Induced emf $= Bv \ell \sin 45 $
$= 0.3 \times 10^{-4} \times 5 \times 10 \times \frac{1}{\sqrt{2}} $
= $1.1 \times 10^{-3} V$
$= 0.3 \times 10^{-4} \times 5 \times 10 \times \frac{1}{\sqrt{2}} $
= $1.1 \times 10^{-3} V$
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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