A 1.0 m long metallic rod is rotated with an angular frequency of 400 rad s-1 about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field of 0.5 T parallel to the axis exists everywhere. Calculate the emf developed between the centre and the ring.
A 1.0 m long metallic rod is rotated with an angular frequency of 400 rad s-1 about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field of 0.5 T parallel to the axis exists everywhere. Calculate the emf developed between the centre and the ring.
Solution and Explanation
Length of the rod, I = 1 m
Angular frequency, \(\omega\) = 400 rad/s
Magnetic field strength, B = 0.5 T
One end of the rod has zero linear velocity, while the other end has a linear velocity of l\(\omega\).
Average linear velocity of the rod, \(v\) = \(\frac{l\omega+0}{2}\)= \(\frac{l\omega}{2}\)
Emf developed between the centre and the ring,
e = Blv=\(Bl\bigg(\frac{l\omega}{2}\bigg)\) = \(\frac{Bl^2\omega}{2}\)
= \(\frac{0.5\times(1)^2\times400}{2}\) =100 V
Hence, the emf developed between the centre and the ring is 100 V.
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Concepts Used:
Faradays Laws of Induction
There are two laws, given by Faraday which explain the phenomena of electromagnetic induction:
Faraday's First Law:
Whenever a conductor is placed in a varying magnetic field, an emf is induced. If the conductor circuit is closed, a current is induced, known as the induced current.
Faraday's Second Law:
The Emf induced inside a coil is equal to the rate of change of associated magnetic flux.
This law can be mathematically written as:
∈\(-N {\triangle \phi \over \triangle t}\)
