A 1.0 m long metallic rod is rotated with an angular frequency of400 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 metallicring. A constant and uniform magnetic field of 0.5 T parallel to theaxis exists everywhere. Calculate the emf developed between the centre and the ring.
Given: The length of the rod is 1 m , the angular frequency is 400 rad/sec and the magnetic field strength is 0.5 T .
The average liner velocity of the rod is given as,
v = 0 + ω l 2 = ω l 2
Where, the angular frequency is ω and the length is l .
The induced emf is given as,
e = B l v = B l ( ω l 2 ) = B l 2 ω 2
Where, the magnetic field is B and the average linear velocity is v .
By substituting the given values in the above expression, we get
e = 0.5 × 1 2 × 400 2 = 100 V
Thus, the induced emf between the centre and the ring is 100 V .
Given: The length of the rod is
The average liner velocity of the rod is given as,
Where, the angular frequency is
The induced emf is given as,
Where, the magnetic field is
By substituting the given values in the above expression, we get
Thus, the induced emf between the centre and the ring is
