A pair of adjacent coils has a mutual inductance of \(1.5~\text H.\) If the current in one coil changes from \(0\) to \(20~\text A\) in \(0.5~\text s,\) what is the change of flux linkage with the other coil?

An air-cored solenoid having a length of \(30\) cm whose area is \(25   \text{ cm}^{2} ,\) and the number of turns is \(500\) carries a current of \(2.5\) A. Suddenly the current is turned off and the time taken for it is \(10^{- 3}  \text{ s} .\) What would be the average value of the induced back-emf across the ends of the open switch in the circuit? (Neglect the variation in the magnetic field near the ends of the solenoid.)