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You know that for a current to flow in a circuit, it must be connected to a point of potential difference such as a battery.
There is an alternative, which relies on the relationship between electricity and magnetism: we can use changes in magnetic flux in order to induce an electromotive force (EMF) and (if the circuit is closed) a current.
Michael Faraday discovered that when the flux passing through a conducting loop changes, an electromotive force (EMF) is induced. This is known as Faraday's Law, and it can be written mathematically:
Not that N is the number of loops experiencing a change in flux, e.g. a solenoid. The EMF can result in a charge separation and a voltage, and if the loop forms a closed circuit, in a current. The size of the current depends on the resistance of the circuit and follows Ohm's Law:
What is the meaning of the negative sign in Faraday's Law. The answer is expressed by Lenz's law, which states that the induced EMF (and current) will be in such a direction that the flux it creates will oppose the change that caused it.
SOURCE: Adapted from Matrix Education: Electromagnetism, URL: https://www.matrix.edu.au/beginners-guide-year-12-physics/electromagnetism/
A handy guide to the generator effect from five minute physics
SOURCE: Five Minute Physics on YouTube, posted on 5 Jun 2017, URL: https://youtu.be/67PktyElHmo
A handy guide to the generator effect and Lenz's law from five minute physics.
SOURCE: Five minute Physics on Youtube, posted 20 Jun 2017, URL: https://youtu.be/FTUWZ8MEy6M
Faraday's Law; Ohm's Law; Lenz's Law; Eddy currents;
Current: Moving charges along a wire or in any conductive material, like the current in a river or cars in the street.
Dipole: Two electric charges or magnetic poles that have the same strength but are opposite in sign or polarity (North versus South) and are separated by a small distance.
Effect: Something brought about by a cause; a result.
Electric charge: A physical state based on the amount and location of electrons and protons in matter. Matter with more electrons than protons is negatively charged. Matter that attracts free electrons is positively charged.
Electric circuit: A system that connects electrical components so that they will operate.
Electric current: A flow of electric charge.
Electric Flux, ΦE : A crowd of electric field lines flowing into a surface area, calculable by multiplying the field by the area. Oh, and angle matters too: 
EMF: Electromotive force.
Magnet solenoid: A solenoid magnet is a coil of insulated wire, usually cylindrical in shape and with a length greater than its diameter. An electric current passing through the solenoid produces a magnetic field similar to that of a bar magnet.
Magnetic field: A region of space near a magnetized body or electrical current where magnetic forces can be detected.
Magnetic field lines: These lines are a way to show the structure of a magnetic field. A compass needle will always point along a field line. The lines are close together where the magnetic force is strong, and spread out where it is weak.
Magnetism (Electromagnetism): A physical property of an object that shows attraction for iron, as in a magnet. Electromagnetism acts between particles with an electric charge, such as electrons, protons, and ions. It is associated with moving electricity, and it creates fields of force.
Magnetometer: An instrument that measures the magnitude (strength) and direction of a magnetic field.
Transformer: an electrical device that transfers electrical energy between two or more circuits through electromagnetic induction.
