Question:
A boy peddles a stationary bicycle the pedals of the bicycle are attached to a $200$ turn coil of area $0.10\, m^{2}$. The coil rotates at half a revolution per second and it is placed in a uniform magnetic field of $0.02 \,T$ perpendicular to the axis of rotation of the coil. The maximum voltage generated in the coil is
A boy peddles a stationary bicycle the pedals of the bicycle are attached to a $200$ turn coil of area $0.10\, m^{2}$. The coil rotates at half a revolution per second and it is placed in a uniform magnetic field of $0.02 \,T$ perpendicular to the axis of rotation of the coil. The maximum voltage generated in the coil is
Updated On: Jul 5, 2022
- $1.26 \,V$
- $2.16 \,V$
- $3.24 \,V$
- $4.12\,V$
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The Correct Option is A
Solution and Explanation
Here $\upsilon=0.5\,Hz, N=200, A=0.1\,m^{2}$
and $B = 0.02\, T$
Maximum voltage generated is
$\varepsilon_{0}=NBA\left(2\pi\upsilon\right)=200\times0.02\times0.1\times\left(2\pi\times0.5\right)$
$=1.26\,V$
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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