Final answer:
The opposite signs of the emf peaks are due to Lenz's law, which causes the induced electromotive force (emf) to always oppose the change in current or magnetic flux that produced it.
Step-by-step explanation:
The sign of the emf of the second peak being opposite to the sign of the first peak is explained by Lenz's law. This law states that the induced emf will always act in a direction to oppose the change that produced it. For example, if the change in current in a coil or the motion of a magnet relative to a coil causes a positive emf at first, reversing that change, such as by changing the direction of the current or the motion of the magnet, will produce an emf with a negative sign, thereby opposing the original change.
Moreover, the induction of an emf is symmetrical. If a current in one coil induces an emf in a second coil, a change in the current in the second coil will induce an emf in the first coil with a polarity that opposes that change. This induction of emf is dependent on the rate of change of magnetic flux through the coil, symbolized by Faraday's law of induction.