The magnetic field in the cylindrical region shown in figure increases at a constant rate of `20.0mT//sec` . Each side of the square loop abcd and defa has a length of `I.00cm` and a resistance of `4.00Omega` . Find the cuurent (magnitude and sense) in the wire ad if:
(a) the switch `S_(I)` is closed but `S_(2)` is open
(b) `S_(I)` is but `S_(2)` is closed
(c) both `S_(I)` and `S_(2)` are open and
(d) both `S_(I)` and `S_(2)` are closed

Explanation

(a)
`(dB)/(dt)=20mT//sec=20xx10^(-3)T//sec`
Flux through loop `adef`
`phi=BA`
`e=(dphi)/(dt)=(dB)/(dt)l^(2)`
`=(20xx10^(-3))(1xx10^(-2))^(2)=20xx10^(-7)V`
Resistance of loop `R=4xx4=16Omega`
Current in the loop `I=(e)/(R)=(20xx10^(-7))/(16)=1.25xx10^(-7)A`
Since flux is increasing, induced current will be anticlockwise i.e. `a` to `b`
(b) Same current, anticlockwise in the loop `a b c d` , `d` to `a`
(c) No current
(d) Current in `ad` : zero