Electric Charges and Fields - Summary

Experiencing sparks or crackling sounds when removing synthetic clothes, especially in dry weather, is due to electric discharge.
Lightning during thunderstorms is another example of electric discharge.
Electric shocks from car doors or bus bars are caused by accumulated electric charges discharging through the body.
Electrostatics studies forces, fields, and potentials from static charges.

Thales of Miletus (600 BC) discovered amber rubbed with wool attracts light objects.
Electricity is derived from the Greek word elektron, meaning amber.
Rubbing certain pairs of materials causes them to attract light objects.
Like charges repel, and unlike charges attract.
Polarity differentiates the two kinds of charges.
Benjamin Franklin named charges as positive and negative.

Bodies like glass or plastic rods, silk, fur, and pith balls become electrified when rubbed.
Electrified objects lose their charge when brought into contact.
Objects with no charge are electrically neutral.
Gold-leaf electroscope detects charge by divergence of gold leaves.
Materials are normally electrically neutral but contain balanced charges.
Electric force is pervasive, holding molecules and atoms together.
Electrifying a neutral body involves adding or removing charges, specifically electrons.
A positively charged body loses electrons, while a negatively charged body gains electrons.

Conductors allow electricity to pass through easily (e.g., metals, human bodies, earth).
Insulators resist the passage of electricity (e.g., glass, plastic, wood).
Semiconductors have intermediate resistance.
Charge distributes over the entire surface of a conductor but stays in place on an insulator.

Point charges are charged bodies with sizes much smaller than the distances between them.
Charges add algebraically like real numbers (scalars).
Total charge of a system is the sum of individual charges: $q = q1 + q2 + q3 + … + qn$ .
Charge is conserved; it can neither be created nor destroyed, only transferred.
Charge is quantised, meaning it exists in integral multiples of a basic unit e: $q = ne$ , where n is an integer.
The basic unit of charge, e, is the charge of an electron or proton.
In SI units, charge is measured in coulombs (C).
$e = 1.602192 × 10^{-19} C$
Macroscopic charges are much larger than e, making quantisation unnoticeable.

Describes the quantitative force between two point charges.
The force (F) between two point charges $q1$ and $q2$ separated by distance r in a vacuum is:
$F = k \frac{q1 q2}{r^2}$
$k ≈ 9 × 10^9 Nm^2C^{-2}$
In SI units, $k = \frac{1}{4πε0}$ , where $ε0$ is the permittivity of free space.
$ε_0 = 8.854 × 10^{-12} C^2N^{-1}m^{-2}$
Coulomb's law in vector notation:
$F{21} = \frac{1}{4πε0} \frac{q1 q2}{r{21}^2} \hat{r}{21}$
Like charges: repulsion, unlike charges: attraction.
Coulomb's law agrees with Newton’s third law.

The force on a charge due to multiple charges is the vector sum of forces due to individual charges (Superposition Principle).
$F1 = F{12} + F{13} + … + F{1n}$
$F1 = \frac{1}{4πε0} \sum{i=1}^{n} \frac{q1 qi}{r{i1}^2} \hat{r}_{i1}$

A charge Q produces an electric field everywhere around it.
The electric field at a point r due to charge Q is:
$E(r) = \frac{1}{4πε_0} \frac{Q}{r^2} \hat{r}$
The force F on charge q due to electric field E is $F = qE$
The SI unit of electric field is N/C.
Electric field is independent of the test charge q.
For a system of charges, the electric field is the vector sum of electric fields due to individual charges.
$E(r) = \frac{1}{4πε0} \sum{i=1}^{n} \frac{qi}{ri^2} \hat{r}_i$

Used to represent the electric field pictorially.
The direction of the field line indicates the direction of the electric field.
The density of field lines represents the strength of the electric field.
Field lines start from positive charges and end at negative charges.
In a charge-free region, electric field lines are continuous curves without breaks.
Two field lines never cross each other.
Electrostatic field lines do not form closed loops.

Pair of equal and opposite charges, q and -q, separated by a distance 2a.
Dipole moment vector $p = q × 2a$
Direction: from -q to q.
The electric field of a dipole at large distances:
- On the dipole axis: $E = \frac{2p}{4πε_0r^3}$
- On the equatorial plane: $E = \frac{-p}{4πε_0r^3}$
  where r >> a

Electric field due to an infinitely long straight uniformly charged wire:
$E = \frac{λ}{2πε_0r}$
Electric field due to a uniformly charged infinite plane sheet
$E = \frac{σ}{2ε_0}$
Electric field due to a uniformly charged thin spherical shell:
- Outside the shell (r > R): $E = \frac{q}{4πε_0r^2}$
 $E = 0$ where r < R

Here are the formulas and their names from the provided text:

Total charge of a system: $q = q1 + q2 + q3 + … + qn$
Charge quantization: $q = ne$
Coulomb's Law: $F = k \frac{q1 q2}{r^2}$
Coulomb's law (in SI units): $k = \frac{1}{4πε*0}$
Permittivity of free space: $ε_0 = 8.854 × 10^{-12} C^2N^{-1}m^{-2}$
Coulomb's law in vector notation: $F{21} = \frac{1}{4πε0} \frac{q1 q2}{r{21}^2} \hat{r}{21}$
Superposition Principle: $F1 = F{12} + F{13} + … + F{1n}$
Superposition Principle (summation): $F1 = \frac{1}{4πε0} \sum{i=1}^{n} \frac{q1 qi}{r{i1}^2} \hat{r}_{i1}$
Electric field due to a point charge: $E(r) = \frac{1}{4πε_0} \frac{Q}{r^2} \hat{r}$
Force on charge q due to electric field E: $F = qE$
Electric field due to multiple charges: $E(r) = \frac{1}{4πε0} \sum{i=1}^{n} \frac{qi}{ri^2} \hat{r}_i$
Electric flux: $Φ = E · ΔS = E ΔS cos θ$
Dipole moment vector: $p = q × 2a$
Electric field of a dipole on the dipole axis: $E = \frac{2p}{4πε_0r^3}$
Electric field of a dipole on the equatorial plane: $E = \frac{-p}{4πε_0r^3}$
Gauss's Law: $Φ= q/ε_0$
Electric field due to an infinitely long straight uniformly charged wire: $E = \frac{λ}{2πε_0r}$
Electric field due to a uniformly charged infinite plane sheet: $E = \frac{σ}{2ε_0}$
Electric field due to a uniformly charged thin spherical shell (outside the shell): $E = \frac{q}{4πε_0r^2}$
Electric field due to a uniformly charged thin spherical shell (inside the shell): $E = 0$