FARADAY’S LAWS

CONTENTS

Faraday’s LifeMagnetic FluxExperiments of FaradayLenz lawMotional EMFEddy CurrentSelf InductanceMutual InductanceApplications of Faraday LawGeneratorInduction StoveElectric Guitar

History of Faraday(1791 - 1867)• Born to a poor family in Newington, • England

• Diligent and intelligent

• He became an errand boy for a• bookbinding shop and he read every • book that he bound

• He became interested in the concept of force,or specifically force

• Because of his early reading and experiments with the idea of force,he was able to make important discoveries in electricity later in life

• Wrote to Sir Humphry Davy• Chemist at the Royal

Institution• Begged for a job and sent

along with a bound volume of notes, which he had taken at Davy’s lectures

• Impressed by the boy’s zeal, Davy made Faraday his laboratory assistant in 1813

Big Change in Faraday’s life

Big change (continued)

Since then (21 year-old), drank in knowledge from Davy

Finished his second apprenticeship in 1820 Great accomplishment for a man who was almost

completely self-educated originally

BASIC TERMINOLOGY

Magnetic Flux

Magnetic flux represents how closely together magnetic field lines are packed.

A

B

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

Magnetic flux (Contd…)

Φm = A.B

Φm = AB cos θ

Units: 1 weber = 1Wb = 1Tm2

GRAPHICAL INTERPRETATION OF MAGNETIC FLUX

The magnetic flux is proportionalto the number of field lines that passthrough 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.dSarea

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

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

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

FARADAY’S EXPERIMENT(CONTD)

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.

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.

IMPORTANT CONCLUSIONS

Faraday’s Law of Induction

N S

iv

i

i/t

S

EMF

Ɛ = - FB /t

The emf induced around a loop

equals the rate of changeof the flux through that loop

Moving the magnet changes the flux FB

Changing the current changes the flux FB

Faraday Law: changing the flux induces an emf.

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:

[1 loop only]

[ For N loops]

Faraday’s Law of Induction (contd…)

This drawing shows the variables in the flux equation:

VARIABLES OF THE FLUX EQUATION

Magnetic flux will change if the area of the loop changes:

CHANGING THE VARIABLE A

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.

CHANGING THE VARIABLE ‘θ’

The -ve sign gives

the direction of

The induced EMF

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.

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 theinduced emf).

This is easier to use than to say ...Decreasing magnetic flux emf creates additional

magnetic fieldIncreasing 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.

This image shows another way the magnetic flux can change:

EMF Induced in a Moving Conductor

The induced current is in a direction that tends to slow the moving bar – it will take an external force to keep it moving.

EMF Induced in a Moving Conductor

What happens when the conducting horizontal bar falls?

EMF Induced in a Moving Conductor

1.As the bar falls, the flux of B changes , so a current is induced, and the bulb lights.

2.The current on the horizontal bar is in a magnetic field , so it experiences a force , opposite to gravity

When current is induced in a bulk piece of conductor, the induced current often flows in small circles that are strongest at the surface and penetrate a short distance into the material. These current flow patterns are thought to resemble eddies in a stream, which are the tornado looking swirls of the water that we sometimes see. Because of this presumed resemblance, the electrical currents were named eddy currents.

These circulating eddies of current have inductance and thus induce magnetic fields. These fields can cause repulsive, attractive and heating effects.

Eddy Current

Eddy Current

Eddy currents

Eddy currents are undesirable as they heat up the conductor and dissipate electrical energy.Hence we always try to minimise the eddycurrents by laminating the metals or by cutting slots in the metal piece as shown.

The effect in which a changing current in a circuit induces and emf in the same circuit is referred to as self induction.

Self inductance

t

IL

E

self inductance

SI Unit of self inductance: (Henry) H 1As1V

Self inductance

The changing current in the primary coil creates a changingmagnetic flux through the secondary coil, which leads to aninduced emf in the secondary coil.

The effect in calledmutual induction.

Mutual induction

tN

E

t

IM

psE

Emf due to mutual induction

mutual inductance

SI Unit of mutual inductance: (Henry) H 1As1V

Mutual induction

APPLICATIONS OF

FARADAY’S LAW

Faraday’s law gives rise to countless technological

applications. The law has far-reaching consequences

that have revolutionized the living of mankind after its

discovery. Faraday’s discovery of electromagnetic

induction has numerous industrial, technological,

medical and other applications. Some of them are

briefed as follows:

ELECTRIC GENERATORS

Electric Generators

A generator transforms mechanical energy into electrical energy. This is an ac generator:

The axle is rotated by an external force such as falling water or steam. The brushes are in constant electrical contact with the slip rings.

 

When the coil is rotated with a constant angular speed ω, the magnetic field vector B and the area vector A of the coil at any instant t is θ=wt(assuming θ=0° at t=0). As a result the flux Φ changes. The flux at any time t is given as

Φ = Bacosθ = BAcosωt

From Faradays law, the induced EMF for the rotating coil of N turns is then

E = -N dΦ/dt = -NBA d(cosωt)/dtThus the instantaneous value of EMF is

Derivation of the emf induced

Electric Generators

Electric Generators(contd.)

Variation of EMF with rotation of the coil

Induction stoveThe pan on the stove is heated by eddy currents produced by induction.

An ac current in a coil in the stove top produces a changing magnetic field at the bottom of a metal pan.

The changing magnetic field gives rise to a current in the bottom of the pan.Because the pan has resistance, the current heats the pan. If the coil in the stove has low resistance it doesn’t get hot but the pan does.

An insulator won’t heat up on an induction stove.

Induction stove

Induction Stove

In induction cooking container’s size, shape and positioning is very important to achieve maximum output

Only Ferromagnetic materials like enameled steel, cast iron and stainless steel designed for induction can be used for induction cooking.

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.

The ac voltage in the primary coil causes a magnetic flux change given by

.BP P

Δφ = N

ΔtV

The changing flux (which is efficiently “carried” in the transformer core) induces an ac voltage in the secondary coil given by

.BS S

Δφ = N

ΔtV

Dividing the two equations gives the transformer equation

.S S

P P

N =

N

VV

A “step up” transformer increases the output voltage in the secondary coil; a “step down” transformer reduces it.

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).

.S P

P S

N =

N

II

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, 

In, practice real transformer are less than 100% efficient.

Resistive losses in the coils which can be reduced by making their cross section large and by using high purity copper. Eddy currents losses in the core which can be reduced by laminating the core .Laminations reduce the area of circuits in the core, and so reduce the emf and current flowing in the core and energy is lost. Hysteresis losses in the core. The magnetisation and demagnetisation curves for magnetic material are often a little different and this means that the energy required to magnetise a core(while current is increasing) .The difference in energy is lost as heat in the core. Geometric design as well as material of the core may be optimised to ensure that the magnetic flux in each coil of the secondary is nearly the same as that in each coil of the primary.

LOSSES IN TRANSFORMER

Electric guitar

A magnetic pickup consists of a permanent magnet with a core of material such as alnico or ceramic, wrapped with a coil of several thousand turns of fine enameled  copper wire.

The pickup is most often mounted on the body of the instrument.

The permanent magnet magnetizes the steel strings above it

ELECTRIC GUITAR (CONTD…)

The output of the amplifier is sent to the loudspeaker, which produces the sound wave we hear. when the string vibrates at some frequency, its magnetized segment produces a changing flux through the coil. The changing flux induces an emf in the coil that is fed to an amplifier. The output of the amplifier is sent to the loudspeaker, which produces the sound wave we hear.

ELECTRIC GUITAR (CONTD…)

Flash light

Thank you