A metallic rod of 2 ~m length is rotated with a frequency 100 ~Hz about an axis passing through the centre of the circular ring of radius 2 ~m . A constant magnetic field 2 ~T is applied parallel to the axis and perpendicular to the length of the rod. The emf developed across the ends of the rod is :

Step-by-step solution

The induced emf e across a rod of length l rotating with angular velocity in a uniform magnetic field B perpendicular to the plane of rotation is given by the formula e = 1 2 B l^2 . Given parameters are: Length of the rod l = 2 m Frequency f = 100 Hz Magnetic field B = 2 T The angular velocity is calculated as = 2 f = 2 100 = 200 rad/s . Substituting these values into the formula: e = 1 2 2 (200 ) (2)^2 e = 1 200 4 e = 800 V . Answer: 800 volt