In a very long solenoid of radius `R`, if the magnetic field chabges at the rate of `dB//dt.AB = BC`
The induced emf for the trianglar circuit `ABC` shown in Fig. 3.196 is

Options

A. (a) `R^(2)((dB)/(dt))`
B. (b) `4R^(2)((dB)/(dt))`
C. ( c) `(1)/(2)R^(2)((dB)/(dt))`
D. (d) `2R^(2)((dB)/(dt))`

Answer

A

Explanation

(a)`|E| = (dphi)/(dt) = A(dB)/(dt) = 2[(1)/(2)R R] (dB)/(dt) = R^(2)(dB)/(dt)`
In loop `ABC`, emf induced due to branch `AC` is zero and contribution of emf due to `AB and BC` are equal, hence contribution of emf for the branch is
`|E|_(AB) = (R^(2))/(2)((dB)/(dt))`