Flow of charges.

$Q=Q_{+}-Q_{-}$

$\quad \quad \propto$ time $t$

Rate of flow

$\quad \quad I=\frac{Q}{t}$

$\Delta t$

$\Delta Q$

$I(t)=\text{Lim}_{\Delta t \rightarrow 0} \frac{\Delta Q}{\Delta t}=\frac{d Q}{d t}$

$\text { Units } \frac{\text { Coulomb }}{\text { Second }}=\text { Ampere }$

S.I. A Fundamental SI unit.

220-240V Household appliances. $\sim 5 \text { A }$

Several Thousand Ampere

Fish $\sim 1$ A

Human Nervous System $\mu A$

Similarity with flow of water through a pipe

Positive +

Negative -

Rub a piece of amber with fur.

Pressure, Temperature

Conductors,(Silver, Copper, Aluminium Hg)

Readily conduct electricity

Eletron gas, Free electrons

Belong to whole material

electrostatics : Conductors

$\vec{E}_{inside}=0$ : Not true under dynamic conditions

NaCl Ionic compounds

$Na{\rightarrow}Na^{+} + e^{-}$

$Cl + e^{-}{\rightarrow}Cl^{-}$

Insulators

Tightly bound electrons.

$E_{inside}$ need not be zero

Semiconductors

Metals Electrostatics

Charge pump

No internal electric field will be created.

$E_{int}$ = 0

Hence charge flow current.

Direction of flow of positive charge

$I$ has a direction but is a scalar

$\frac{dQ} {dt}$ = I

Q = through a surface

• = $\int {Idt}$

Current Density is a vector

|J| = $\frac{I}{Area}$

Since $\vec{J}$ is a vector, we need to give a direction

$\overrightarrow{d S}$ : a direction perpendicular to the cross section

$\vec{J}$ : In the direction of current flow

$\vec{J}.\vec{dS}$ > 0

For positive current

No electric field.

Thermal velocity $\sim$ ${10^6}$ m/s

$\vec{E}_{inside}=0$

Elastic collision

Velocities of different electrons are uncorrelated.

$\frac{1}{N} \sum_{i=1}^N\left\langle\vec{v}_i\right\rangle=0$

Average velocity of the collection of electrons is Zero.

$\vec E_{inside} \neq 0$.

Electrons are accelerated

The collection of electrons would move in a direction opposite to $\vec{E}$

All electrons within a volume AL will pass through that right face

n = electron density

Q = (en)LA

e = Magnitude of electron charge = 1.6 x $10^{19}$ c

|J|= $\frac{Q}{A t} = e n \frac{L}{t} = en v_\alpha$

• ${\vec{J}=-e n \vec v_\alpha}$