If the current in coil A is 'switched on' or 'switched off', then an electric current is induced in the coil B (see Figure given here). This can be explained as follows:

(i) When we switch on the current in the coil A, through switch S, it produces a magnetic field around the coil B and in this way coil A becomes an electromagnet and produces a magnetic field around coil B. The change would also be seen on inserting a magnet into the coil B. So, an induced current flows in coil B for a moment. When the current in coil A becomes steady, its magnetic field also becomes steady and the current in coil B stops.

(ii) When we switch off the current in coil A, then its magnetic field in coil B stops quickly. This effect is just the same as pulling a magnet quickly out of coil B. So, in this case an induced current flows in coil B in the opposite direction.