TF EIM Chapt1

Fundamentals

Charge

Every stable and independent object (particle) that has charge has been observed to contain a quantized unit of charge which is a multiple of [math]\displaystyle{ 1.6 \times 10^{-19} Coulombs }[/math]

What are the obervations/experiments?

Experiment 1: Matter is composed of Atoms with a positively charged nucleus surround by negatively charged electrons. If we now the charge of one mole of electrons ([math]\displaystyle{ F }[/math]= Faradays constant) and the number of electrons in a mole ([math]\displaystyle{ N_A }[/math] = Avagadros number)then the charge of a single electron is given by

[math]\displaystyle{ e = \frac{F}{N_A} }[/math]

Experiment 2: Oil drop experiment

Experiment 3: The Hall Effect and the Josephson Effect

Coulomb

The amount of charge that flows through any cross section of a wire in 1 second if there is a steady current of 1 ampere in the wire.

Coulomb Force

Two charged object separated by a distance (d) will feel a force between them known as the coulomb force. The magnitude of this force has been experimentally shown to be

[math]\displaystyle{ \left | \vec{F}_{coul} \right | = \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r^2} }[/math]

where

[math]\displaystyle{ \varepsilon_0 =\frac {1}{\mu_0 c_0^2}=8.854187817 \times 10^{-12} }[/math]F/m = a experimentally measured quantity satisfying the above relationship know as the permittivity of free space.

[math]\displaystyle{ q_1 = }[/math] charge of first object

[math]\displaystyle{ q_2 = }[/math] charge of second object

[math]\displaystyle{ r = }[/math] distance between the charges

(Charles Augustin Coulomb first measured the attract and repulsive force between two charged objects using a torsion balance around 1785)

This force may be described in terms of an electric field E such that

[math]\displaystyle{ \vec{E} = \frac{\vec{F_q}}{q} }[/math]

Where

F= force between the objects

Electric Field

Vector Field

What is a vector field?

A vector field is the association of each point in space with a direction (vector)

Example: Gravity. One the surface of the earth you observe that an apple will fall down to the ground. You can define a vector ([math]\displaystyle{ \vec{g}) }[/math] which points directly down and tell you the direction that an apple will accelerate if it is released. If you construct [math]\displaystyle{ \vec{g} }[/math] such that

[math]\displaystyle{ \vec{g} = \frac{F_g}{m} = \frac{\frac{GMm\vec{r}}{r^3}}{m} = \frac{GM\hat{r}}{r^2} }[/math] = acceleration of an apple towards the earth's surface when close to the earth's surface.

Consider what you observe when you place a bar magnet in the vacinity

A separated object of finite charge creates an electric field.

Ohm's Law

resistance is a constant

[math]\displaystyle{ R = \frac{\Delta V}{I} }[/math]= constant

Voltage

The MKS unit for Voltage is a Joule per Coulomb [math]\displaystyle{ \left ( \frac{\mbox{J}}{\mbox{C}}\right ) }[/math]

Voltage in circuits is typically defined as the electric potential energy per unit charge relative to ground.