Faraday's law of induction is based on Michael Faraday's experiments in 1831 and gives the relation between the rate of change of the magnetic flux through the area enclosed by a closed loop and the electric field induced along the loop:
where E is the induced electric field, ds is an infinitesimal element of the closed loop and dΦB/dt is the rate of change of the magnetic flux. Or, in differential form in terms of magnetic field B:
In the case of an inductor coil where the electric wire makes N turns, the formula becomes:
where V is the induced electromotive force and ΔΦ/Δt denote the change of magnetic flux Φ during the time interval Δt. The direction of the electromotive force (the negative sign in the above formula) was first given by Lenz's law.
He also states that An EMF is inducted when the magnetic field around a conductor changes in his first law and The magnitude of the induced emf is proportional to the rate of change of the flux linkage in his second.
Faraday's law, along with the other laws of electromagnetism, was later incorporated into Maxwell's equations, unifying all of electromagnetism.
Automotive example of Faraday's law of induction:
A practical automotive example of Faradays law is contained in automotive ignition systems which use an induction coil, to step up the nominal battery voltage of 12 volts to the voltage needed to bridge the gap across the spark plug electrodes. Relative movement between a conductor and a magnetic field allows four ways by which an electro-motive force, or EMF, can be induced in a conductor.
Move a magnet so that the magnetic lines of force cut across a conductor. As in an alternator.
Move the conductor so that it cuts across the stationary magnetic field. As in a generator.
Start, stop or change the rate of current flow in a conductor. This causes the conductor to induce an EMF into itself. This is called self induction.
Start, stop or change the rate of current flow in a conductor which is positioned close to a second conductor. This is called mutual induction.
When any of these methods is used to induce voltage in a conductor, the value of that voltage depends on the density, or strength, of the magnetic field. The stronger the field, the greater the induced voltage. It is also influenced by the number of turns of the coil.
The greater the number of turns, the greater the induced voltage. The speed at which the lines of force are cut also effects the voltage induced.
The greater the speed, the greater the induced voltage.
In the induction coil, the secondary winding has many thousands of turns of fine enameled copper wire. The primary winding with a few hundred turns of relatively heavy wire is positioned close to the secondary. A soft iron core is positioned centrally to concentrate the magnetic field. Current flow through the primary winding establishes a magnetic field around the windings.
The higher the current flow, the stronger the field.
Sudden interruption of the primary current effectively disconnects the battery from the coil and current flow ceases. This leaves no externally applied voltage source to dictate the voltage value across the ends of the primary winding. The magnetic field decreases, returning it's stored energy to the coil by cutting across the coil windings.
This produces a self-induced voltage in the primary winding and a mutually induced voltage in the secondary winding.
Faraday’s First Law states that An EMF is induced when the magnetic field around a conductor changes. Faraday’s Second Law states that the magnitude of the induced EMF is proportional to the rate of change of the flux linkage.
Then, if this coil is 100 percent efficient, the maximum voltage available from the secondary winding would be 300 volts multiplied by 100. That is 30,000 volts. Since the value of the self-induced voltage in the primary winding is also influenced by the rate of change of current flow through the coil, it is essential to switch the primary current off as quickly as possible. All ignition systems make provision to ensure that this occurs.
Source: CDX Global & Wikipedia - en.wikipedia.org
