Two main approaches to build or learn a theory:

1) Inductive, or historical approach: you learn Electromagnetics by studying the history of it. This is an empirical approach.

2) Deductive, or axiomatic approach: you start from some unproven relations or postulates and build the theory. This is an abstract approach.

Needs for a theory:

A theory allows us to predict phenomena from the knowledge of other phenomena.

A crucial component of any theory is its range of applicability. The better that range is defined, the better the theory.

Theres nothing more practical than a good theory.

Three steps are involved in building a theory on an idealized model within the deductive approach.

1) some basic quantities related to the subject of study are defined: Electric charge q, Electric Field Intensity E, Force F

2) the rules of operation (the mathematics) of these quantities are specified: = cos().

3) some fundamental relations are postulated: = .

Starting only from the postulates in point 3), we build sequences (i.e. theories) of equations relating only the quantities in point 1) using only the rules in point 2). The predictions of the resulting equations are compared with reality in controlled experiments. If they do not match we need new postulates and/or rules and/or quantities.

Heres how it works:

Easy as pie.

We use the symbol (sometimes ) to denote electric charge

= 1.619 1019 (C)

The principle of conservation of electric charge must be

satisfied at all times and under any circumstances

Volume charge density: () = lim0

() (C m3 )

charge of one electron:

The electric charge can be represented as dimensionless points (point charges) or, more conveniently, through a continuous function ()of the position :

() = lim0

() (C m2 )

() = lim0

() (C m ) Line charge density:

Surface charge density:

The scalar electric current is the rate of change of charge with respect to time:

=

(C/s or A)

The electric current can be also described by a vector:

The volume current density: J (A/m2)

Is the amount of current per unit area (the magnitude of J) flowing through a unit area normal to direction of current flow (the direction of J).

In the case of a sheet current, one can define another vector:

The surface current density: Js (A/m)

There are four fundamental vector field quantities in electromagnetics:

symbols and units for field quantities

Field quantity Symbol Unit

Electric Electric field intensity E V/m

Electric flux density (Electric displacement)

D C/m2

Magnetic Magnetic flux density B T

Magnetic field intensity H A/m

When there is no time variation (as in static, steady, or stationary

cases), the electric field quantities and and the magnetic field

quantities and form two separate vector pairs.

In time-dependent cases, however, electric and magnetic field

quantities are coupled; that is, time varying and will give rise to

and , and vice versa.

All four quantities are point functions; they are defined at every point

in space and, in general, are functions of space coordinates.

All the units used in electromagnetics, are derived units expressible in terms of meters, Kilograms, seconds, and amperes.

In our electromagnetic model there are three universal constants:

3 108 (m/s)

0 =1

36 109 8.854 1012 (F/m)

0 = 4 107 (H/m)

= 0, =1

0,

We will see that, in free space,

=1

00 (m/s)

1. Velocity of electromagnetic wave in free space

2. Permittivity of free space,

3. Permeability of free space,

How to build a theory: the deductive (or axiomatic) approach

Basic ingredients: Quantities, Rules, Axioms

Scalars: point charge, charge distributions

Vectors: electric (E, D) and magnetic (B, H) fields

Constants: c, e0, m0 .