A cycle wheel of radius $0.5\, m$ is rotated with constant angular velocity of $10 \,rad/s$ in a region of magnetic field of $0.1\, T$ which is perpendicular to the plane of the wheel. The $EMF$ generated between its centre and the rim is,
- 0.25 V
- 0.125 V
- 0.5 V
- zero
The Correct Option is B
Solution and Explanation
The formula to calculate emf is
\(E = \frac{B \omega l^2}{2}\)
\(E\) is the electromotive force (EMF) generated.
\(B\) is the magnetic field strength (0.1 Tesla in this case).
\(l\) is the length, 0.5m
ω is the angular velocity (10 radians per second).
To calculate the value of EMF, let's put the values in the formula:
\(E = \frac{B \omega l^2}{2}\)
\(=\frac{0.1(10)(0.5)^2}{2} = 0.125\,v\)
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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