A rectangular loop of wire moving through a magnetic field is a common example used to illustrate the principle of energy conservation in the context of motional electromotive force (EMF).

Suppose that the rectangular loop is initially at rest, and is then pulled to the right through a uniform magnetic field. As the loop moves through the magnetic field, a motional EMF is induced, which causes an electric current to flow in the wire.

This current, in turn, generates a magnetic field that opposes the original magnetic field. According to Lenz’s law, the direction of the induced magnetic field is such that it opposes the original magnetic field. This means that the induced magnetic field will be directed to the left, and will cause a force to be exerted on the loop in the opposite direction to its motion.

This force acts to slow down the motion of the loop, and it will eventually come to a stop. At this point, the induced magnetic field will have reached its maximum value, and the loop will have converted all of its kinetic energy into electrical energy.

If the loop is then moved back to its original position, a motional EMF in the opposite direction is induced, which causes a current to flow in the opposite direction. This current generates a magnetic field that now aids the original magnetic field, and the loop is pulled back to its starting position.

In this way, the loop has converted its initial kinetic energy into electrical energy, and then back into kinetic energy again, without any net loss of energy. This illustrates the principle of energy conservation, which states that energy cannot be created or destroyed, but only converted from one form to another.

Overall, the example of a rectangular loop moving through a magnetic field provides a simple but powerful illustration of the principle of energy conservation, and the role of motional EMF in converting kinetic energy into electrical energy, and vice versa.