A spinning copper disc is slowed down when a magnet is brought near it. Note that copper is not a magnetic material.

Eddy currents are induced in the disc due to the relative motion of the disc and the magnet. The magnetic fields associated with these currents have such a direction that they oppose the cause that created them in the first place (Lenz rule). As a result they oppose the relative motion between the disc and the magnet and hence the disc is slowed down.

The current drawn by a simple motor may vary in time depending on what the motor does at any given instant.

1. When a motor is connected to a battery, the current in the coil (or armature) increases dramatically but as soon as the coil starts rotating increasingly faster, the current drops and settles at a certain value. This is because of the so-called "back emf" induced in the coil as it rotates in a magnetic field (Faraday's law). The back emf has such polarity that it opposes the emf of the cell (Lenz's law).

2. When the motor spins and there is no load attached, the current stays constant. (The value of the current is I = (emf_cell - back_emf)/R where R is the total resistance of the circuit, including any internal resistance of the battery)

3. When the motor does work on an external load and it slows down, the back emf drops as its value depends on how fast the armature spins. As a result, the current through the motor increases up to a value that depends on how "hard" the motor works.

This video shows a simple circuit consisting of a light bulb and a variable resistor (rheostat). The voltmeter measures the voltage across the terminals of the battery: V = emf - Ir, where emf is the electromotive force of the battery, I is the electric current in the circuit and r is the internal resistance of the battery.  When the switch is open, I = 0 and V = emf. When the switch is closed, a current flows through the circuit and V = emf - Ir. V can also be calculated as IR where R is the total resistance of the circuit. If R is increased, I decreases and V increases (as the product Ir gets smaller and V = emf - Ir). 

This video shows a couple of torches/flashlights that use electromagnetic induction to function. They do not need batteries. The second part of this video shows a simple handheld electric generator which is one of the most common applications of electromagnetic induction. The video also shows that the electric generator is nothing else than an electric motor used in reverse (i.e. instead of putting a current through a coil placed in a magnetic field in order to obtain motion, we turn the coil in a magnetic field in order to generate an induced current).

When a magnet is moved in or out of a coil, a current is induced in the coil. The size of the induced current depends on how fast the magnet is moved. The direction of the induced current depends on the polarity of the magnet and on the direction in which the magnet moves (i.e. towards the coil or away from the coil). The size of the induced emf (voltage) across the two ends of the coil can be determined from Faraday’s law. The “polarity” of the induced emf can be determined from Lenz’s law.

A current-carrying conductor placed in a magnetic field experiences a force. The direction of this force depends on the direction of the magnetic field and the direction of the electric current. If the conductor is perpendicular to the magnetic field lines, the size of the force can be calculated using the formula F = B x I x L where B is the magnetic field strength, I is the electric current and L is the length of the conductor in the magnetic field.

This effect is sometimes called the “motor effect” as it is the basic principle behind an electric motor.

When a current passes through a conductor or a coil, a magnetic field is created in the surrounding space. Its presence can be revealed by using a compass needle. Changing the direction of the current changes the polarity of magnetic field produced.