ELECTROSTATICS

Electric Charges & Fields

Use: Notes + Revision

Charge

Basics

Quantization of charge: Q = n e, n = 1,2,3…
e = 1.6 × 10^-19 C
Additivity of charge
Superposition (net effect = sum of effects)
Redistribution of charge (after contact)

Example: If charge = 1 nC ⇒ electrons count = Q / e

Charge Density

Units

Linear: λ = Q / L (C/m)
Surface: σ = Q / S (C/m²)
Volume: ρ = Q / V (C/m³)

Tip: Pick formula by shape (line/surface/volume)

Coulomb’s Law

Force

F = (1 / 4π ε₀) × (Q₁Q₂ / r²)

Like charges: repulsion
Unlike charges: attraction
ε₀ = permittivity of free space
In medium: F_medium = F_air / K

Equilibrium of Charges

Net Force = 0

Condition: net force on a charge must be zero
Common setup: charges on a line, find neutral point / balancing charge
Outside region: closer to smaller magnitude charge (rule used in many cases)

Idea: Set |F₁| = |F₂| with correct directions

Neutral point depends on magnitudes and positions of charges.

Electric Field

E Field

E = (1 / 4π ε₀) × (Q / r²)

Force on charge: F = qE
Direction (as given): for + charge, towards the point where E is evaluated; for - charge, away
Superposition: E_net = E₁ ± E₂

Special: If E₁ = E₂ and angle = 120° ⇒ E_net = E

Properties of Field Lines

Rules

Start from positive and end on negative
Never intersect
Always perpendicular to conducting surface
More density ⇒ stronger electric field
Never form closed loops

Extra: Lines count ∝ |q|

Electric Flux & Gauss Law

Flux

Flux: Φ = ∫ E·dS cosθ
Gauss Law: Φ = q_net / ε₀
Zero flux when q_net = 0

Meaning: Flux ∝ total field lines passing through surface

Electric Flux for a Cube (Common Cases)

Shortcuts

No charge inside cube ⇒ Φ = 0
Charge at center ⇒ Φ_total = q/ε₀, one face = q/(6ε₀)
Charge at face center (on surface) ⇒ Φ_cube = q/(2ε₀)
Charge at corner ⇒ Φ_cube = q/(8ε₀)
Charge at edge ⇒ Φ_cube = q/(4ε₀)

Rule: Symmetry share = total flux / number of equal parts

Application of Gauss’s Theorem (Field Results)

E Results

Point charge: E = Kq/r²
Metal sphere / hollow sphere: outside E = KQ/r², inside E = 0
Non-conducting sphere: inside field increases with r, outside like point charge
Conducting sheet / non-conducting sheet: field depends on surface charge density
Infinite line charge: E = 2Kλ/r
Circular arc/ring: field at center depends on angle and symmetry

Note: These are the standard results listed in your mind map.

Charged Particle in Electric Field

Motion

Acceleration: a = qE/m
If released along field: speeds up in field direction
If released opposite: slows down
If velocity ⟂ field: gets deflected (path changes)

Velocity change: v = (qE/m) t (basic case)

Charge on Pendulum

Balance

tanθ = (qE) / (mg)
So, q = (mg tanθ) / E
Small angle: sinθ ≈ tanθ ≈ θ (in radians)

Quick: bigger E ⇒ bigger deflection