Why does an electric drill heat up when passing through metal compared to in thin air?

To understand why the drill produces more heat we must understand Lenz's law. Lenz's law states that the direction of an induced current is always such as to oppose the change that causes the current. In the drill motor, current is passed through metal brushes to an inner, rotating coil within a magnetic field. When a charge moves within a magnetic field, perpendicular to the field lines, a force is acted on the moving charge by the field. The force acts perpendicular to the direction of both the field lines and the direction of the moving charge (as shown by Faraday's left-hand rule). As the current is the flow of multiple charges through the coil, the accumulative force on each side of the coil creates a couple around a pivot, causing it to rotate.This shows that when emf (voltage) is supplied from the drill’s power supply, the coil rotates. However, as there is charge moving within a magnetic field, emf is also generated in the coil in the opposite direction to that of the supplied emf. This is known as “back-emf” and is shown by Faraday's right-hand rule and the equation ε ∝ 2πf, where ε is the emf and f is the frequency of the coils’ rotation. This demonstrates Lenz's law as the induced emf created by the coil’s rotation is now opposing the initial change of emf in the coil from the power supply. This must be the case, otherwise the velocity of the coil would increase towards infinity which cannot happen due to the law of conservation of energy.When there is very little resistance at the end of the drill (air resistance only), the emf induced in the coil due to the motion of the coil and drill bit is near equal to the emf supplied by the power supply. As both emf’s flow in opposite direction to each other, they cancel each other out. This causes little current to flow through the coil and therefore minor heat emission due to resistance.This all changes however, when the resistance at the end of the drill is increased, for example when drilling into metal, as now the drill bit moves slower and so does the coil. This causes the back-emf to decrease. However, the emf from the power supply remains the same, causing the resultant emf and current in the coil to increase, and therefore more heat to be emitted due to resistance.