The magnetic field in the cylindrical region shown in increases at a constant rate of 20.0 mT/s. Each side of the square loop abcd and defa has a length of 1.00 cm and a resistance of `4.00 Omega`. Find the current (magnitude and sense) in the wire ad if (a) the switch `S_1` is closed but `S_2` is open, (b) `S_1` is open but `S_2` is closed, (c) both `S_1` and `S_2` are open and (d) both `S_1` and `S_2` are closed.

Explanation

(a) When `S_1 closed and S_2 open`
`Net R=4xx4=16 Omega`
`e=(d phi)/(dt)=A.(dB)/(dt)`
`=10^(-4)xx2xx10^(-2)`
`=2xx10^(-6)V`
`Through ad=e/R= (2xx10^(-6))/16`
`=1.25xx10^(-7) A along ad.`
` (b)Here R= 16 Omega`
`e=Axx(dB)/(dt)=2xx10^(-6)V`
`i=(20xx10^(-6))/(16)`
`=1.25xx10^(-7) A along da.`
`(c) since both S_1 and S_2 are open , no current is passed as circuit is open i,e.`
`i=0`
`(d) Since both S_1 and S_2 and are closed, the circuit forms a balance wheatstone bridge and no current will flow along ad i.e,`
`i=0`.