Presentation Of Electromagnetic theory

Presented To :- Sir. Umer

Group Members

M Mateen Shahid Saqlain Ahmed Mir Behroz Laraib satakzai M. Sadiq

Three Laws of Electromagnetism

These 3 major laws are related to Magneto static Fields

All of them are inter related with each other These laws are applied to solve the current

distribution

Faraday’s Law

Faraday’s Law

In 1831, Michael Faraday, an English physicist gave one of the most basic laws of electromagnetism called Faraday's law of electromagnetic induction.

This law shows the relationship between electric circuit and magnetic field.

Faraday performed an experiment with a magnet and coil. He found how emf is induced in the coil when flux linked with it

changes.

Faraday’s Experiment Faraday took a magnet and a coil and

connected a galvanometer across the coil. At starting, the magnet is at rest, so there is

no deflection in the galvanometer i.e needle of galvanometer is at the center or zero position.

When the magnet is moved towards the coil, the needle of galvanometer deflects in one direction.

When the magnet is held stationary at that position,

the needle of galvanometer returns back to zero position.

Faraday’s Law

Now when the magnet is moved away from the coil, there is some deflection in the needle but in opposite direction and again when the magnet becomes stationary,

At that point with respect to coil, the needle of the galvanometer returns back to the zero position.

Similarly, if magnet is held stationary and the coil is moved away and towards the magnet, the galvanometer shows deflection in similar manner.

It is also seen that, the faster the change in the magnetic field, the greater will be the induced emf or voltage in the coil.

Faraday’s Law

Important ConclusionWith 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’s Law

Michael Faraday formulated two laws on the basis of above experiments. These laws are called Faraday's laws of electromagnetic induction.

Faraday’s First Law:“Any change in the magnetic field of a coil of wire will cause an emf to be induced in the coil. This emf induced is called induced emf and if the conductor circuit is closed, the current will also circulate through the circuit and this current is called induced current.”

Faraday’s Law

Faraday’s Second Law: Faraday’s second Law states that

“The magnitude of emf induced in the coil is equal to the rate of change of flux that linkages with the coil. The flux linkage of the coil is the product of number of turns in the coil and flux associated with the coil.”

Mathematically, the rate of change of flux linkage is equal to induced emf.

EMF=E= -dФB

dt

Where ФB is the magnetic flux, given as:

ФB= ∫ B. dA

The minus sign is due to Lenz’s Law that states that the direction of the induced emf is such that it opposes the change in flux.

For N number of turns

EMF= -N. dФB

dt

Faraday’s Law

Applications: 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:

Faraday’s Law

Applications:

Electric Generator:

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.

Magnet Recording

Transformer: Electric Guitar “ A transformer is a device for

increasing or decreasing an ac voltage.”

When AC voltage is applied on primary coil, it induces voltage in secondary coil.

Applications:

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 permanent magnet magnetizes the steel strings above it.

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.

Ampere’s LawThis Law states that“ For any closed loop path, the sum of the length elements times the magnetic field in the direction of the length element is equal to the permeability times the electric current enclosed in the loop.”Mathematically: Ʃ B.ΔL=µo. I

Where µo=4 × 10-7 T m/A and is called the permeability of free space. ΔL is small segment of perimeter, and B is the magnetic field Parallel to ΔL.

Ampere’s Law

Consider a closed path in the form of a circle of radius ‘r’. This closed path is referred as Amperean path. Divide this path into small elements of length ΔL.Let B be the value of flux density at the sight of ΔL, and ϴ is the angle between B and ΔL:

Consider the Integral.

Applications of Ampere’s Law:Following are applications of Ampere’s Law:

Long straight wire

straight conductor carrying current

Toroidal coil

Solenoid

The Biot-Savart Law

BioT and Savart recognized that a conductor carrying a steady current produces a force on a magnet.

Biot and Savart produced an equation that gives the magnetic field at some point in space in terms of the current that produces the field.

Biot-Savart law says that if a wire carries a steady current I, the magnetic field dB at some point P associated with an element of conductor length ds has the following properties: The vector dB is perpendicular to both dl

(the direction of the current I) and to the unit vector r directed from the element ds to the point P.

The magnitude of dB is inversely proportional to r2, where r is the distance from the element ds to the point P.

The magnitude of dB is proportional to the current I and to the length ds of the element.

The magnitude of dB is proportional to sinθ , where θ is the angle between the vectors ds and r.

Biot-Savart law:

2

o

rπ4r̂xdsIμ

dB

μo is a constant called the permeability of free space; μo =4· x 10-7 Wb/A·m (T·m/A)

Biot-Savart law gives the magnetic field at a point for only a small element of the conductor ds.

To determine the total magnetic field B at some point due to a conductor of specified size, we must add up every contribution from all elements ds that make up the conductor (integrate)!

2o

rr̂xds

π4Iμ

dB

The direction of the magnetic field due to a current carrying element is perpendicular to both the current element ds and the radius vector rhat.

The right hand rule can be used to determine the direction of the magnetic field around the current carrying conductor: Thumb of the right hand in the

direction of the current. Fingers of the right hand curl

around the wire in the direction of the magnetic field at that point.

Application: Magnetic Field of a Thin Straight Conductor

Consider a thin, straight wire carrying a constant current I along. To determine the total magnetic field B at the point P at a distance a from the wire:

Use the right hand rule to determine that the direction of the magnetic field produced by the conductor at point P is directed out of the page.

This is also verified using the vector cross product (ds x r): fingers of right hand in direction of ds; point palm in direction of r (curl fingers from ds to rhat); thumb points in direction of magnetic field B.

The cross product (ds x r) = ds·r·sin ; q r is a unit vector and the magnitude of a unit vector = 1.

(ds x r) = ds·r·sin = q ds·sin q

Each element of length ds is a distance r from P and a distance x from the midpoint of the conductor O. The angle q will also change as r and x change.

The values for r, x, and q will change for each different element of length ds.

Let ds = dx, then ds·sin q becomes dx·sin .q

The contribution to the total magnetic field at point P from each element of the conductor ds is:

2o

rθsindx

π4Iμ

dB

The total magnetic field B at point P can be determined by integrating from one end of the conductor to the other end of the conductor.

The distance from the midpoint of the conductor O to the point P remains constant.

Express r in terms of a and x.

Express sin q in terms of a and r.

21

22 xa

ara

θsin

21

22222 xarxar

For an infinitely long wire:

From the table of integrals:

23

22

o

23

22

o

21

2222o

2o

2o

xa

dxπ4

aIμ

xa

dxaπ4Iμ

B

xa

axa

dxπ4Iμ

B

rθsindx

π4Iμ

rθsindx

π4Iμ

dB

2

12222

322 xaa

x

xa

dx

aπ2Iμ

B

aπ4Iμ2

11aπ4Iμ

aπ4Iμ

B

aπ4Iμ

B

aaaπ4Iμ

B

xa

xaπ4aIμ

xaa

xπ4

aIμB

o

ooo

21

221

2

o

21

2221

22

o

21

222o

21

222

o

For a conductor with a finite length:

From the table of integrals:

x

x

x

x

x

x

x

x

x

x

x

x

23

22

o

23

22

o

21

2222o

2o

2o

xa

dxπ4

aIμ

xa

dxaπ4Iμ

B

xa

axa

dxπ4Iμ

B

rθsindx

π4Iμ

rθsindx

π4Iμ

dB

2

12222

322 xaa

x

xa

dx

21

22

o

21

22

o

21

2221

22

o

21

2221

22

o

x

21

222o

x

21

222

o

xaaπ2

xIμB

xa

x2aπ4Iμ

B

xa

x

xa

xaπ4Iμ

B

xa

x

xa

xaπ4Iμ

B

xa

xaπ4aIμ

xaa

xπ4

aIμB

xx

Thank You