CBSE Class 12-science Answered

Method I

As the rod is rotated, free electrons in the rod move towards the outer end due to Lorentz force and get distributed over the ring. Thus, the resulting separation of charges procures an emf across the ends of the rof. At a certain value of emf, there is no more flow of electrons and a steady state is reached. Using eq., the magnitude of the emf generated across a length dr of the rod as it moves at right angles to the magnetic flied is given by

de = Bv. Hence,

OR

Method II

To calculate the emf, we Can imagine a closed loop OPQ in which point O and P are  connected with R and OQ is the rotating rod. The potential difference across the resistor is then equal to the induced emf and equals B x (rate of change of area of loop) Ifθ is the angle between the rod and the radius of the circle at P at time t, the area of the sector OPQ is given by

where R is the radius of the circle. Hence, the induced emf is