Question:
A metal conductor of length $1 \,m$ rotates vertically about one of its ends with an angular velocity $5 \,rad\, s^{-1}$. If the horizontal component of earths magnetic field is $0.2 \times10^{-4}\,T$, then the emf developed between the ends of the conductor is
A metal conductor of length $1 \,m$ rotates vertically about one of its ends with an angular velocity $5 \,rad\, s^{-1}$. If the horizontal component of earths magnetic field is $0.2 \times10^{-4}\,T$, then the emf developed between the ends of the conductor is
Updated On: May 20, 2024
- $5\, \mu\,V$
- $5\,m\,V$
- $50\, \mu \, V$
- $50\,m\,V$
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The Correct Option is C
Solution and Explanation
The emf developed between the ends of the conductor is
$\varepsilon=\frac{1}{2}\omega Bl^{2}=\frac{1}{2}\times5\times0.2\times10^{-4}\times(1)^{2}$
$=5\times10^{-5}\,V=50\times10^{-6}V$
$=50\, \mu\,V$
$\varepsilon=\frac{1}{2}\omega Bl^{2}=\frac{1}{2}\times5\times0.2\times10^{-4}\times(1)^{2}$
$=5\times10^{-5}\,V=50\times10^{-6}V$
$=50\, \mu\,V$
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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