A metallic rod of 10 ~cm is rotated with a frequency 100 revolution per second about an axis perpendicular to its length and passing through its one end in uniform transverse magnetic field of strength 1 ~T . The emf developed across its ends is:

Step-by-step solution

The induced electromotive force (emf) across the ends of a conducting 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: = 1 2 B l^2 Given values are: Length l = 10 cm = 0.1 m Frequency f = 100 rev/s Magnetic field B = 1 T The angular velocity is related to frequency f by: = 2 f = 2 100 = 200 rad/s Substituting these values into the emf formula: = 1 2 1 (200 ) (0.1)^2 = 1 2 200 0.01 = 100 0.01 = V Using 3.14 , we get: = 3.14 V