FUNDAMENTALS

ELECTROSTATICS:
All bodies are able to take a charge of electricity, and this is known as

static electricity. The charge on the body is measured by means of

the force between the two charges, this force following the inverse square law

( i.e ) the force is proportional to the product of the charges and inversely

Proportional to the square of the distance between them.

This may be written as F=q1q2/4╥ﻉ○d² N

Where q1 and q2 are the charges in coulombs and d the distance in metres- the

Space in between the charges being either air or a vacuum with permittivity ﻉ○.

N is Newtons.

If the two charged bodies are separated by some other medium the force acting

may be different, depending upon the relative permittivity of the dielectric

between the two charged bodies.

The relative permittivity is termed as dielectric constant.

In this case force F= q1q2/ 4╥ﻉŗﻉ○ d² N

whereﻉŗ is the constant for the particular dielectric. For Air or Vacuum the value

ofﻉŕ is Unity..

ELECTROSTATIC POTENTIAL:

The potential to which the body is rasied by an electric charge is

proportional to the charge and the capacity of the body so that C=Q/V where V is

the potential and C is the capacity.

The capacity of a body is defined as the charge or quantity of electricity

necessary ro raise the potential by one volt.

This unit of potential is the work done in joules, in bringing unit charge

(1coulomb) from infinity to a point at unit potential.


CAPACITANCE:

The actual measurement of capacity is termed as capacitance, and for

practical purpose the unit is arranged for use with volts and coulombs. In this

case the unit of capacitance is the farad, and we get C=Q/V, where C is in

farads, Q in coulombs and V in volts.

Since, farad is large unit, we employ “ microfarad= 10¯6 “ of a farad or

picofarad=10¯12 of a farad.

CAPACITORS;

The capacity of the body is increased by its proximity to earth or to

Another body and the combination of the two is termed as Capacitor.

So long as there is a potential difference between the two there is a capacitor

action which is affected by the dielectric constant of the material in between the

two bodies.



PLATE CAPACITOR:

Flat plate capacitors are made up of metal plates with paper or

other material as dielectric. The rating of plate capacitor is found from

C =ﻉŗﻉ○A/D farads.


CONCENTRIC CAPACITOR:

With electric cables we get what is equivalent to concentric

capacitors with the outer conductor or casing of radius “r1”m and the inner

conductor of r2 m.


here, C= 2╥ﻉŗﻉ○/ logﻉ( r1/r2) farad per metre.


Values of ﻉŗ for different Materials.

Air 1 Glass 7

Paper,press board 2 Marble 8

Cotton tape( rubbered) 2 Rubber 2.5

Empire cloth 2 Ebonite 2.5

Paper ( oiled) 2 polyethylene 2.3

Shellac 3

Bakelite 6

Paraffin-wax 3

Mica 7

Porcelain 7




CAPACITORS IN SERIES:

C = I/ 1/C1+1/C2=1/C3+ …….

CAPACITORS IN PARALLEL

C = C1+C2+C3+……..


THE MAGNETIC CIRCUIT

ELOECTROMAGNETS:

Magnetism is assumed to take the form of lines of Force which flow round the

magnetic circuit The circuit may be complete path of Iron or consists of an iron

path with one or more air gaps.

The Transformer is an example of the former and Generator the latter.

The Lines of force are proportional to the Magneto-motive-force of the electric

circuit. And this is given by ,mmf=IN/10 ampere turns, where I is the current in

amperes and N is the number of Ampere turns in the coil or coils. This mmf is

similar to emf of an electric circuit and in the place of resistance we have the

Reluctance which may be termed the resistance of the magnetic circuit to the

passage of the lines of force.

Reluctance = S = l / A μŗ μ○ At/ wb, Where l is the length of the magnetic circuit

in millimetres.A is area of cross section in square millimetres and μŗ μ○ is the

permeability of material. The permeability is a property of the actual magnetic

circuit and not only varies with the material in the circuit but with the lines of

force actually induced in the material if that is iron.




The actual flux induced in any circuit is proportional to the ratio

Mmf/reluctance and so we get total flux = Φ = mmf/S wb.

The Relative permeability μ, is always given as the ratio of the number of the

lines of force induced in a circuit of any material compared with the number of

lines induced in air for the same conditions.

The permeability of air is taken as unity and hence, the permeability can be

taken as the magnetic conductivity compared with air.

Substituting values for mmf and S ,

Total flux = Φ= μ ŗ μ○INA/10 l Wb.

Flux density = B= Φ/A tesla (T), Tesla is one Weber per square metre.

Magnetic leakage coefficient = flux in air –gap/ flux in iron.

AMPERE- TURNS PER METRE ( At/m)

In order to deal with complex magnetic circuits such as Generators, Motors etc.,

it is more convenient to take the various sections of the magnetic circuits

separately , and for this purpose it is useful to have the ampere-turns required

per metre to give a fixed flux density.

Taking the formula of Total flux, we get

B =Φ/A = μŗμ○ IN/10 l = μŗμ○H

So that the permeability and flux density are linked by the expression

IN/10 l = H, which is called the magnetizing force and it will be seen that this is

Equal to the ampere-turns per unit length (i.e. Metre). The relation between

B and H is given by B-H curve

FUNDAMENTALS

INTENSITY OF FIELD:

There is an electrostatic field due to any charged body and the intensity of this

field is taken as the force on unit charge.

The intensity of field at any given point due to an electrostatic charge is given by

E= q / 4╥ﻉ○ d² V/m

AMPERE

The value of the ampere is defined as that current which, when flowing in each

of the two infinitely long parallel conductors in a vacuum, separated by one

meters from centres, causes each conductor to have a force acting upon it of

2 x 10−² N/m lenghth of conductor.

DIELECTRIC FLUX:

The field due to a charge as referred to the above is assumed to be due to

imaginary tubes of force similar to the magnetic lines of force and the tubes are

the paths which would be taken by a free unit charge if acted on by the charge of

the body concerned.

By means of these tubes we get a dielectric flux density of so many tubes of

Force per square metre of area. Let us take a spere of 1 metre radius and give it

unit charge of electricity. We get a dielectric flux density on the surface of sphere

of unit = one tube of force per square centimeter. The total number of tubes of

force will be equal to the surface area of the sphere=4 ╥

For any charge ‘q’ at a distance ‘r’ the dielectric flux density will be

D = q/ 4 ╥ŗ² C/m²

There fore intensity of electric field is E = q/4 ╥ﻉ○ﻉŗ² i.e E= D/ﻉŗ○