There is a uniform magnetic field `B` in a circular region of radius `R` as shown in Fig. 3.149 whose magnitude changes at the rate of `dB//dt`. The emf circular concentric conducting arc of radius `R_(1)` having an angle `theta` as shown `(-OAO' = theta)` is

Options

A. `(theta)/(2pi)R_(1)^(2)(dB)/(dt)`
B. `(theta)/(2)R^(2)(dB)/(dt)`
C. `(theta)/(2pi)R^(2)(dB)/(dt)`
D. none of these

Explanation

Required emf `=piR^(2)(dB)/(Dt)*(theta)/(2pi)`
`:. E=(R^(2))/(2R_(1))((dB)/(dt))`
`emf=(theta)/(2pi)(R^(2))/(2R_(1))((dB)/(Dt))2piR_(1)=(theta)/(2)R^(2)((dB)/(dt))`