A conducting rod rotates with a constant angular velocity `'omega'` about the axis which passes through point 'O' and perpendicular to its length . A uniform magnetic field 'B' exists parallel to the axis of the rotation . Then potential difference between the two ends of the rod is :-

Options

A. `(B l^2 omega)/(2)`
B. 0
C. `((Bl^2 omega)/(8))`
D. `2Bl^2 omega `

Answer

B

Explanation

Length of the rod between the axis of rotation and one end of the rod =l/2
Area swept out in one rotation ` = pi (l/2)^2 = ((pi l^2)/(4))`
Angular velocity ` = omega rad s^(-1)`
Frequency of revolution ` =(omega)/(2pi)`
Area swept out per second ` = (pi l^2)/(4) ((omega)/(2pi)) = (l^2 omega)/(8)`
Magnetic induction = B
Rate of change of magnetic flux ` = ((Bl^2 omega)/(8))`
Magnitude of induced emf ` = (Bl^2 omega)/(8)`
Magnitude of induced emf between the axis and the other and is also `((Bl^2 omega)/(8))`. These two emfs are in opposite directions. Hence , the potential difference between the two ends of the rod is zero.