A rod of length `l` rotates with a uniform angular velocity `omega` about its perpendicular bisector. A uniform magnetic field B exists parallel to the axis of rotation. The potential difference between the two ends of the rod is

Options

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

Answer

B

Explanation

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