Build-up to Modern Theory
In 1831Michael Faraday (1791-1867) began a series of experiments that led to him to an equation that linked electricity and magnetism. This relationship is now known as Faraday's Law. It states that 'The inducded Electromotive Force or EMF in any closed circuit is equal to the time rate of change of the magnetic flux through the circuit.' (Meissner; p.50)
With this relationship Faraday showed that changing magnetic fields induce electric currents.
James Clerk Maxwell proved the inverse, that a flow of electric current is also surrounded by a magnetic field (Meissner; p.50). The Biot-Savart Law describes the magnetic field generated by a current. The flow of the magnetic field through a wire can be determined by the right hand rule.
Right Hand Rule
Induced Magnetic Field in a Loop of Wire