# Introduction a potential difference (voltage) across a conductor

IntroductionIt was first discovered that current in a wire produces a magnetic field andthen Michael Faraday discovered that the opposite is also true in that amagnetic field can produce a current inside a conductor.Electromagnetic Induction is the production of a potential difference (voltage)across a conductor when it is exposed to a changing magnetic field. When aconductor is moved across a magnetic field so as to cut through the lines ofmagnetic flux, an electromotive force (emf) is produced in the conductor. Magneticflux is how any material is affected by a magnetic field.

The moving magneticfield caused by the changing magnetic flux induces emf however the measure ofmagnetic flux is not important, it is whether or not there’s change in fluxover time.If the conductor forms part of a closed circuit then the emf produced causes electronsto flow round the circuit thus a current is produced.When a magnetic field associated with a magnet, moves towards a coil of wire,the magnetic flux of the magnet moves across or cuts the coil. It is therelative movement of the magnetic flux and the coil that causes an emf and thuscurrent to be induced in the coil.·        When the magnet is moved at a constant speedtowards and/or through the coil, the galvanometer moves showing that currenthas been produced in the coil.

·        When the magnet is moved at the same speed asbefore but away from the coil, the same movement on the galvanometer is seen butin the opposite direction.·        When the magnet is motionless, even within thecoil, the galvanometer does not move.·        When the coil is moved rather than the magnet atthe same speed as before and the magnet is held stationary, it results in thesame galvanometer measurement as before.

·        When either the speed of the magnet or coil isdoubled whilst the other is stationary, it results in a doubled galvanometermeasurement.·        When a stronger magnet is used, it results in agreater measurement.·        When the number of turns of wire of the coil isincreased, it results in a greater measurement. LawsFaraday’s First Law: Any changein the magnetic field of a coil of wire will cause an emf to be induced in thecoil. With this induced emf if the conductor circuit is closed, current willalso circulate through the circuit and this current is called induced current.

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Faraday’s Second Law: The magnitudeof emf induced in the coil is equal to the rate of change of flux that linkswith the coil. The flux linkage of the coil is the product of number of turnsin the coil and flux associated with the coil.Lenz’s Law: An electric current,induced by a source such as a changing magnetic field, always creates acounterforce opposing the force inducing it.Fleming’s Hand Rules: Used to aid inthe understanding of magnetic field, motion and induced current directions.

Fleming’sleft-hand rule is used for electric motors, while Fleming’s right-hand rule isused for electric generators. Different hands need to be used for motors andgenerators because of the differences between cause and effect. In an electricmotor, the electric current and magnetic field exist (which are the causes),and they lead to the force that creates the motion (which is the effect).

ApplicationsElectromagnetic induction is the fundamental operating principles oftransformers, inductors and many types of electrical motors, generators andsolenoids:In an electric motor, the motor has coils turning inside magnetic fields, and acoil turning inside a magnetic field induces an emf. This emf, known as theback emf, acts against the applied voltage that’s causing the motor to spin inthe first place, and reduces the current flowing through the coils.In AC generators, conductors forming an electric circuit are made to movethrough a magnetic field.

By Faraday’s law an emf is induced in the conductorsand thus a source of emf is created. A generator convert mechanical energy intoelectrical energy.In a transformer, alternating current from primary coil moves quickly back andforth across the secondary coil. The moving magnetic field caused by thechanging flux induces a current in the secondary coil, stepping the voltageeither up or down. FormulaeThe image above shows a conductor moving backwards and forth between a magnet.

The formula used to calculate induced emf is:E = Blv (measuredin volts).B is the flux density measured in tesla, l is the length of the conductormeasured in metres and v is the conductor velocity measured in metres persecond.The equation above assumes the conductor moves through the magnetic field at a90?however when the conductor moves through at an angle ??, the equation is:E = Blv sin?The first equation is for a linear conductor. There are also loop conductors wheretotal emf is doubled, 2Blv sin?. If the loop has numerous turns it is now acoil and the number of turns in the coil, N, must be considered in the equation,therefore the total emf for a loop conductor is:E = 2NBlv sin?InductanceBefore examining inductance, firstly Inductors must be discussed. Aninductors is a components used when the property of inductance is required in acircuit and it is basically a coil of wire. Inductance can be thought of as thechange in current and flux linkages that induces emf in a circuit.

There aretwo types of inductance, self and mutual inductance. Self inductance is whenthe emf is induced in the same circuit as that in which there is a change offlux due to current change and mutual inductance is when emf is induced in acircuit but the change in flux due to current change is in an adjacent circuit.The equations for measuring induced emf in a coil of N turns is: The change in flux, measured in webers in d? and dt is the timetaken for the flux to change in seconds.Taking current into account to actually find the inductance of a coil is givenby: Where L is inductance measured in Henry, change in flux, measured in webers, d? = ? and I iscurrent measured in amperes. Putting those two equations together results in: Where dI is change in current and dt is the time taken for the current tochange.The minus sign in the induced emf equations represents the direction of emfgiven by Lenz’s Law.Going back to inductors, there are a number of factors that affect the inductanceof an inductor including:·        Number of turns in a wire – more turns moreinductance.·        Arrangement of turns – the shorter and thickerthe coil of wire, the higher the inductance.·        Cross-sectional area of the coil of wire – the greaterthe area, the higher the inductance.·        Presence of a magnetic core in the wireAn inductor can store energy,measured in joules, in its magnetic field and to calculate it, the formula is: Another aspect to consider when calculating inductance is Reluctance which isthe magnetic resistance of a magnetic circuit to the presence of magnetic flux,however it is not necessary to know at this point in the understanding ofelectromagnetic induction.