The Electric Void

NODE 01

Electric Phenomenon

• Static shock, lightning, charged comb.
• What property of matter produces this?
• Electric charge.

NODE 02

Electric Charge

vs

• Positive, Negative, Neutral.
• Like charges repel, unlike attract.
• SI unit: coulomb (C).

NODE 03

Charge is Quantized

q=ne

• Occurs in discrete elementary units (e).
• n = integer.
• Macro charge = enormous number of units.

NODE 04

Conservation

• Isolated system: total charge is conserved.
• Charge is transferred, not created/destroyed.

NODE 05

Conductors & Insul

• Conductors: Charge moves freely (Metals).
• Insulators: Charge much less free (Rubber, Glass).

NODE 06

Charging Methods

👐⚡🧲

• Friction, Conduction (contact).
• Induction (redistribution without contact).
• Charging = transferring, not creating.

NODE 07

Electrostatic Force

• The interaction between charges.
• Introduces Coulomb's Law.

NODE 08

Coulomb's Law

F = k|q₁q₂|/r²

• Charge magnitude & inverse-square separation.
• Attractive vs repulsive.
• Electric analogue of Newtonian gravitation.

NODE 09

Electric vs Gravity

F_gMASS (ATTRACT)

F_eCHRG (ATTR/REP)

• Gravity: Masses, attractive only.
• Electric: Charges, attract or repel.
• Electric forces are vastly stronger at micro scales.

NODE 10

Superposition

• F_net = F₁ + F₂ + ... (Vector addition).
• Forces do not simply add as ordinary numbers.

NODE 11

Electric Field (E)

E=F/q

• Force experienced per unit mass... wait, charge.
• Source charge vs Test charge.
• Units: N/C or V/m. Vector field.

NODE 12

Field of Point Chrg

• E = k|Q|/r².
• Away from positive, toward negative.
• Represented with radial field lines.

NODE 13

Field Lines

• Density = strength. Tangent = direction.
• Pos source → Neg source. Never cross.
• Visualizations, not physical strings.

NODE 14

Multiple Charges

• E_net = E₁ + E₂ + ...
• Dipoles, charge distributions.

NODE 15

Electric Dipole

• Equal & opposite charges separated by small dist.
• Dipole moment: p = qd (points - to +).

NODE 16

Dipole in Uniform E

• Experiences torque: τ = pE sinθ.
• PE: U = -pE cosθ.
• Connects to Realm 05 (Torque).

NODE 17

Electric Flux

• Field passing through a surface.
• Φ = E A cosθ.
• Not simply "number of field lines".

NODE 18

Gauss's Law

∮E·dA=Q/ε₀

• Central symmetry tool of electrostatics.
• Relates flux through closed surface to enclosed charge.

NODE 19

Gaussian Surfaces

• Chosen according to symmetry (Sphere, Cylinder, Plane).
• Key skill: recognize symmetry first.

NODE 20

Spherical Dist

• Outside charged sphere, it behaves like point charge at center.

NODE 21

Inside Conductor

• E = 0 inside material in electrostatic equilibrium.
• Free-charge redistributes to the surface.

NODE 22

Shielding

• Conducting enclosures protect interiors from external fields.
• Faraday cages.

NODE 23

Electric Potential

V=W/q

• Scalar energy landscape.
• Work done per unit pos test charge from infinity.
• V = kQ/r.

NODE 24

Potential Diff

• Voltage (ΔV = ΔU/q).
• Electric field points toward decreasing potential.

NODE 25

Electric PE

U = kq₁q₂/r

• U = kq₁q₂/r. Reference at infinity.
• Connects directly to Realm 06 (Work/Energy).

NODE 26

E from V

E= -dV/dx

• E = -dV/dx (or E = -∇V).
• Field points toward decreasing potential.
• Links calculus to physical fields.

NODE 27

Equipotentials

• Surface of constant V.
• Moving charge along it requires zero work.
• E-field is perpendicular to surface.

NODE 28

Conductors & Pot

• Ideal conductor in static eq is an equipotential.
• Same potential throughout.

NODE 29

V of Multiple Chrg

• Potential is scalar: V_tot = V₁ + V₂ + ...
• Unlike Force/Field which require vector addition.

NODE 30

Electrostatic Work

W = -ΔU = -qΔV

• Work done moving charge through E-field.
• E-field transfers energy by moving charges.

NODE 31

PE of Systems

• Summing pairwise interactions (each pair counted once).
• Energy stored in a configuration of charges.

NODE 32

Capacitance

C=Q/V

• Charge stored per potential difference.
• Unit: Farad (F). Depends on geometry & dielectric.

NODE 33

Parallel-Plate

• C = εA/d.
• Area ↑ → C ↑. Separation ↓ → C ↑.

NODE 34

Dielectrics

• Insulating materials between plates.
• Polarization, permittivity. Increases capacitance.

NODE 35

Caps in Series

• 1/Ceq = 1/C₁ + 1/C₂ + ...
• Same charge magnitude, voltage division.

NODE 36

Caps in Parallel

• Ceq = C₁ + C₂ + ...
• Same voltage, charge division.

NODE 37

Energy Stored

U = ½CV²= ½QV= Q²/2C

• Connects electrostatics to Realm 06.

NODE 38

Energy Density

u= ½εE²

• The EM field ITSELF carries stored energy.
• Extremely important for later electromagnetism.

NODE 39

Cap Charging Pre

• Charging/discharging, time dependence.
• Capacitor as energy storage. Realm 16 previews.

NODE 40

Atmos Electricity

• Thunderclouds, charge separation, E-fields.
• Cloud electrification is complex in reality.

NODE 41

Lightning

• Charge sep → strong E-field → breakdown.
• Spark gaps, static discharge.

NODE 42

Electrostatics Tech

🖨️🌫️👆

• Photocopiers, laser printers, precipitators.
• Spray painting, capacitive touch screens.

NODE 43

Force in Biology

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+

-

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• Charged biomolecules, cell membranes, ions.
• Bridge into Biology and Chemistry.

NODE 44

Experiment Lab

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E

V

C

• Friction charging, electroscope, E-field mapping.
• Capacitor charging, Coulomb-law simulation.

NODE 45

Field Vis Chamber

• Visually rich representations (Dipole, uniform field).
• Fields are otherwise invisible.

NODE 46

Graph Chamber

• E vs r (1/r²), V vs r (1/r).
• Q vs V (linear), U vs V (parabolic).

NODE 47

Misconceptions

X

• "Field needs test charge" → No, source creates it.
• "E-field = Force" → E is a property; F needs a charge.
• "V=0 means E=0" → Not necessarily.

NODE 48

Solving Engine

• ID Source → Force (Coulomb) or Field (E=F/q).
• Symmetry? Gauss. Energy? V → U.
• Capacitor? C = Q/V.

NODE 49

Master Map

CHARGE → COULOMBFIELD → FLUX → GAUSSPOTENTIAL → CAPACITANCE

• The complete architecture of electrostatics.

NODE 50

Deep Synthesis

• Gravity: Mass → Field → Potential.
• Electricity: Charge → Field → Potential.
• Unlike mass, charge has +/- (repulsion, shielding).