Question:
A uniform circular metal disc of radius $R$ is rotating about a vertical axis passing through its center and perpendicular to its plane with constant frequency f. If $B_H$ and $B_v$ are horizontal and verticaI components of the Earth's magnetic field respectively, then the induced e.m.f between its center and the rim is
A uniform circular metal disc of radius $R$ is rotating about a vertical axis passing through its center and perpendicular to its plane with constant frequency f. If $B_H$ and $B_v$ are horizontal and verticaI components of the Earth's magnetic field respectively, then the induced e.m.f between its center and the rim is
Updated On: Aug 23, 2024
- $\pi\,B_vfR^2$
- $\pi \,B_HfR^2$
- $\pi B_vfR^2$
- Zero
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The Correct Option is C
Solution and Explanation
$e = \frac{1}{2} BR^2 \omega$ where $\omega = 2 \pi f$
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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