FARADAY’S LAWS

Magnetic Flux A B  In the easiest case, with a constant magnetic field B, and a flat surface of area A, the magnetic flux is FB = B A cos  Units : 1 tesla x m2 = 1 weber Magnetic flux represents how closely together magnetic field lines are packed.

Magnetic flux (Contd…) Magnetic flux is higher for stronger magnetic fields. Strong magnet=more lines. In the easiest case, with a constant magnetic field B, and a flat surface of area A, the magnetic flux is Φm = A.B Φm = AB cos θ Units: 1 weber = 1Wb = 1Tm2 In the easiest case, with a constant magnetic field B, and a flat surface of area A, the magnetic flux is

to the number of field lines that pass through a surface. GRAPHICAL INTERPRETATION OF MAGNETIC FLUX The magnetic flux is proportional to the number of field lines that pass through a surface.

Magnetic flux An electric current arises in a closed wire loop when it is moved through a magnetic field. An arbitrary shaped surface can be placed through the loop and flux calculated. C dS Φ = ∫ B.dS area

Magnetic Flux in a non-uniform field Divide the loop into many small pieces The flux is the sum of all these: Φm =∫B.dA

FARADAY’S EXPERIMENT

FARADAY’S EXPERIMENT Almost 200 years ago, around 1831, Faraday looked for evidence that a magnetic field would induce an electric current with this apparatus:

FARADAY’S EXPERIMENT(CONTD) He found no evidence when the magnet was stationary, but did see a deflection in the galvanometer when the magnet was moved away or towards the coil

In the case where a north pole is brought towards the solenoid the current will flow so that a north pole is established at the end of the solenoid closest to the approaching magnet to repel it (verify using the Right Hand Rule):

In the case where a north pole is moving away from the solenoid the current will flow so that a south pole is established at the end of the solenoid closest to the receding magnet to attract it:

In the case where a south pole is moving away from the solenoid the current will flow so that a north pole is established at the end of the solenoid closest to the receding magnet to attract it:

In the case where a south pole is brought towards the solenoid the current will flow so that a south pole is established at the end of the solenoid closest to the approaching magnet to repel it:

FARADAY’S EXPERIMENT(CONTD) He then changed the: no. of turns of the coil, the relative speed of the magnet and coil the direction of relative motion of the coil and magnet and observed the change in the deflections shown by the galvanometer.

IMPORTANT CONCLUSIONS With the help of his experiment, Faraday drew four important Conclusions, which provided the basis of his law: 1.The galvanometer showed deflection whenever there was relative motion between the magnet and the coil. 2.The deflection was more when the relative motion was faster and less when the relative motion was slower. 3.The direction of the deflection changed if the polarity of the magnet was changed 4.The deflection in galvanometer changes with the change in the number of turns of coil-more the number of turns, greater the deflection.

Faraday Law: changing the flux induces an emf. Faraday’s Law of Induction N S i v i i/t S EMF Moving the magnet changes the flux FB Changing the current changes the flux FB Faraday Law: changing the flux induces an emf. The induced emf in a circuit is proportional to the rate of change of magnetic flux, through any surface bounded by that circuit. Ɛ = - FB /t The emf induced around a loop equals the rate of change of the flux through that loop

Faraday’s Law of Induction The induced e.m.f. in a wire loop is proportional to the rate of change of magnetic flux through the loop. Magnetic flux: Unit of magnetic flux: WEBER ( Wb ) 1 Wb = 1 T·m2

Faraday’s Law of Induction (contd…) [1 loop only] [ For N loops]

CHANGING THE VARIABLE A Magnetic flux will change if the area of the loop changes:

CHANGING THE VARIABLE ‘θ’ Magnetic flux will change if the angle between the loop and the field changes:

CHANGING THE VARIABLE ‘θ’ The magnetic flux is analogous to the electric flux – it is proportional to the total number of lines passing through the loop.

Faraday’s Law of Induction(contd…) A current produced by an induced EMF moves in a direction so that the magnetic field it produces tends to restore the changed field. The -ve sign gives the direction of The induced EMF

Real-life applications The following devices use Faraday's Law in their operation. induction stoves tape players metal detectors transformers

Faraday’s law gives the magnitude and direction of the induced emf, and therefore the direction of any induced current. Lenz’s law is a simple way to get the directions straight, with less effort. Lenz’s Law: The induced emf is directed so that any induced current flow will oppose the change in magnetic flux (which causes the induced emf). This is easier to use than to say ... Decreasing magnetic flux  emf creates additional magnetic field Increasing flux  emf creates opposed magnetic field Lenz’s law

Most Important Point of Faraday’s Law: A changing magnetic field produces or creates an electric field. Two types of electric fields. One is created by charge and the other is created by a changing magnetic field.

Transformer

TRANSFORMER A transformer is basically two coils of wire wrapped around each other, or wrapped around an iron core. “ A transformer is a device for increasing or decreasing an ac voltage.” When an ac voltage is applied to the primary coil, it induces an ac voltage in the secondary coil.

A “step up” transformer increases the output voltage in the secondary coil; a “step down” transformer reduces it. The ac voltage in the primary coil causes a magnetic flux change given by The changing flux (which is efficiently “carried” in the transformer core) induces an ac voltage in the secondary coil given by Dividing the two equations gives the transformer equation

For a step-up transformer, NS > NP and VS > VP (the voltage is stepped up). For a step-down transformer, NS < NP and VS < VP (the voltage is stepped down). A transformer that steps up the voltage simultaneously and steps down the current, and a transformer that steps down the voltage and steps up the current. Energy must be conserved; therefore, in the absence of losses, the ratio of the currents must be the inverse of the ratio of turns. Power in = power out, Vp.Ip = Vs.Is,

RESULTANT MAGNETIC FIELDS