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

Answer

B

Explanation

( b) Rquired emf
`f = (pi R^(2) (dB)/(dt))(theta)/(2pi) = (R^(2) theta)/(2)((dB)/(dt))`