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A magnetic field is a region around a magnetic material or a moving electric charge within which the force of magnetism acts. In this context, magnetic fields are created by electric currents and magnetic dipoles, which exert a force on other currents and dipoles. Imagine a magnetic field as invisible lines that surround a magnet or an electric current. These lines are concentrated near the magnet or wire and become weaker as you move away.
In the given problem, the magnetic field's direction and magnitude are being changed, which affects the loop of wire by altering the magnetic flux passing through it. Notice that magnetic fields have a directional quality where a positive designation means the field lines point away from us, while negative means they point towards us. This directionality is crucial as it influences how the induced effects occur in the system, particularly when the field changes over time.

Electromotive force, commonly referred to as EMF, is a key concept when dealing with electric circuits and electromagnetic fields. Despite its name, it is not actually a force. Instead, EMF is a measure of the energy that drives the flow of electric charges around a circuit.
According to Faraday's Law of Electromagnetic Induction, when there is a change in the magnetic environment of a coil or loop of wire, an EMF is induced. The change can be in terms of the magnetic field strength or the flux through the coil. The formula for calculating the induced EMF \( \mathcal{E} \) is: \[ \mathcal{E} = -\frac{\Delta \Phi}{\Delta t} \] where \( \Delta \Phi \) is the change in magnetic flux and \( \Delta t \) is the change in time over which the flux change occurs. The negative sign indicates that the induced EMF acts in such a way as to oppose the change in flux, as per Lenz's Law.

Lenz's Law is an important principle in electromagnetism that states the direction of an induced EMF will always oppose the change in magnetic flux that produced it. This law is derived from the conservation of energy principle. When a changing magnetic field induces an EMF, it generates a current, which in turn creates a magnetic field of its own. This new magnetic field will act to oppose the original change in magnetic field.
In practical terms, Lenz's Law helps to determine the direction of the induced current in a coil. In the exercise, the final magnetic field was in the opposite direction to the initial magnetic field, signifying that the loop's magnetic environment was reversed. Therefore, by Lenz's Law, the induced current will create its own magnetic field, trying to preserve the original magnetic flux direction. Thus, the current will flow in a direction that counterbalances the change, ensuring energy conservation within the system.