Electromagnetism · 100% marks notes

Method 01 · Component superposition

E is a vector; magnitude-only addition invents false cancellations.

Do this: Resolve each E into axes; never add magnitudes unless collinear and same sense.

Method 02 · Potential-first energy

Scalar V is cheaper than integrating vector force along a path when electrostatic.

Do this: Compute V at the location, then U = qV or W = qΔV.

Method 03 · Dipole angle map

One angle convention prevents torque/PE sign flips.

Do this: Measure θ from p to E; stable equilibrium at θ=0, unstable at θ=π.

Method 04 · Field-line audit

Kills distractors without calculation.

Do this: Test statements with: lines leave +, never cross, density ∝ |E|, closed loops forbidden in electrostatics.

Point-charge field and potential

Looks like: Superposition of E and V for discrete charges

Fast model: E is vector sum; V is scalar sum (choose reference).

Electric dipole

Looks like: Field on axis/equator; torque/energy in uniform E

Fast model: p = qd; τ=p×E; U=−p·E in uniform field.

Potential from field / equipotentials

Looks like: V = −∫E·dl; E=−∇V

Fast model: Integrate along a convenient path; use equipotential shortcuts.

Conductor electrostatics

Looks like: Charge on surface, E=0 inside, V constant

Fast model: Excess charge resides on outer surface of conductor; cavity rules apply.

Method 01 · Symmetry-first surface

Wrong surface makes E unable to factor out of the integral.

Do this: Before formulas, write ‘cylindrical / pillbox / sphere’ matching the charge distribution.

Method 02 · Enclosed-charge filter

Separates flux questions from ‘where is E nonzero’ questions.

Do this: List only charge inside the Gaussian volume; ignore exterior for flux.

Method 03 · Inside–outside split

Q_enc jumps at the charge layer; one formula never covers both.

Do this: For shells/spheres, draw r<R and r>R cases before substituting.

Method 04 · Pillbox sheet move

Converts σ to E with minimal geometry.

Do this: Straddle the sheet; use one face outside (and conductor interior E=0 if applicable).

Symmetric Gauss surfaces

Looks like: Infinite line, sheet, sphere, or shell

Fast model: Choose Gaussian surface matching symmetry; Φ=E·A=q_enc/ε₀.

Charge enclosed bookkeeping

Looks like: Cavity, nonuniform ρ, or partial flux

Fast model: Only charge inside the Gaussian surface counts.

Sheet and plane combinations

Looks like: Parallel infinite sheets σ

Fast model: Each infinite sheet contributes σ/(2ε₀) independent of distance.

Flux without finding E

Looks like: Closed surface flux through parts

Fast model: Total flux fixed by q_enc; use symmetry fractions for faces.

Method 01 · Constraint stamp

Chooses the correct U formula and predicts whether U rises or falls.

Do this: Write ‘Q fixed’ or ‘V fixed’ in the margin before any κ substitution.

Method 02 · Dielectric redraw

Converts geometry puzzles into standard C_eq.

Do this: Split the gap into slabs in series (stack along d) or parallel (side-by-side) capacitors.

Method 03 · Charge ledger

Prevents illegal sharing of Q across parallel plates.

Do this: On parallel branches, V same; on series, Q same — assign unknowns only on the free nodes.

Method 04 · Energy path audit

Stops mixing ½CV² with Q²/(2C) across a process that changed the constraint.

Do this: Compute U_initial and U_final with the same constraint; battery work = ΔU_system + heat if needed.

Network of capacitors

Looks like: Series/parallel reduction; equivalent C

Fast model: Series: 1/C=Σ1/C_i; parallel: C=ΣC_i; redraw stepwise.

Energy and charge sharing

Looks like: Connect capacitors; common V; heat loss

Fast model: Conserve charge on isolated nodes; U=½CV² or Q²/(2C).

Dielectric insertion

Looks like: Slab κ, battery connected vs isolated

Fast model: Connected: V fixed, Q→κQ; isolated: Q fixed, V→V/κ (full fill).

Parallel-plate variations

Looks like: Change d or A with/without battery

Fast model: C=ε₀A/d; track which of Q,V is fixed.

Method 01 · Loop-current assignment

One consistent sign system prevents algebraic chaos.

Do this: Define clockwise currents in independent loops; write ΣE=ΣIR with rise/fall signs fixed once.

Method 02 · Internal-r first

Stops treating E as terminal voltage under load.

Do this: Redraw every cell as ideal E in series with r before combining.

Method 03 · Reduce then restore

Faster than full Kirchhoff when symmetry allows.

Do this: Collapse obvious series/parallel, solve outer current, then expand to find branch currents.

Method 04 · Element-local power

Total supply power is not the heat in one bulb.

Do this: Compute I through the named resistor, then P=I²R for that R only.

Series–parallel resistor network

Looks like: Find R_eq, current split, or power

Fast model: Reduce network; use V=IR and current division.

Kirchhoff loop–node

Looks like: Multi-loop with cells and internal r

Fast model: ΣV=0 around loops; ΣI=0 at nodes; include internal r.

Cells in series/parallel

Looks like: Battery packs, identical/non-identical cells

Fast model: Series: add emf and r; parallel identical: emf same, r/n.

Joule heating and instruments

Looks like: H=I²Rt; galvanometer ↔ ammeter/voltmeter

Fast model: Shunt for ammeter; series multiplier for voltmeter.

Method 01 · Ampere symmetry gate

Stops fake ∮B·dl = B·2πr on asymmetric currents.

Do this: Use Ampere only when |B| is constant on the Amperian path by symmetry.

Method 02 · Right-hand direction lock

Force direction errors dominate wrong options.

Do this: Determine B direction before magnitude; mark × / · on the figure.

Method 03 · Uniform-B loop split

Prevents claiming translation from uniform B alone.

Do this: Net F=0 on closed loop in uniform B; keep τ=m×B.

Method 04 · Meter partition

One current-split picture covers both conversions.

Do this: Galvanometer full-scale I_g through G; excess current through shunt, excess voltage on series R.

Biot–Savart / Ampere field

Looks like: Wire, loop axis, solenoid, or sheet

Fast model: Use Ampere when symmetry is high; Biot–Savart for finite pieces.

Lorentz force on charge/wire

Looks like: F=q(v×B) or Iℓ×B; cyclotron radius

Fast model: Keep vector directions; r=mv/(qB) for ⊥ motion.

Magnetic moment and torque

Looks like: Loop μ=IA; τ=μ×B; U=−μ·B

Fast model: Find area vector; then μ and torque/energy.

Force between current elements

Looks like: Parallel wires attraction/repulsion

Fast model: F/L = μ₀ I₁ I₂ /(2πd); same direction attracts.

Method 01 · Lenz-before-magnitude

Direction MCQs die before algebra; magnitude follows from |dΦ/dt|.

Do this: Ask ‘flux increasing or decreasing through whom?’ then mark induced current direction.

Method 02 · Flux inventory

Prevents treating constant B as inducing when only orientation language is decorative.

Do this: Write Φ = B A cosθ with which of B, A, θ varies; differentiate only that factor.

Method 03 · Transient boundary values

Gives I(0), I(∞) without solving DE when only endpoints asked.

Do this: At t=0⁺ inductor current continuous; capacitor voltage continuous. At t→∞, L short, C open for DC.

Method 04 · Energy agency check

Links mechanical power Fv to electrical I²R in rails problems.

Do this: Name who does work against magnetic drag when flux is forced to change.

Faraday flux rule

Looks like: ε = −dΦ_B/dt for loop in changing B or area

Fast model: Compute Φ=B·A; differentiate; apply Lenz for direction.

Motional emf

Looks like: Rod on rails, rotating rod, or sliding bar

Fast model: ε = Bℓv for ⊥ geometry; or ∫(v×B)·dl.

Self and mutual inductance

Looks like: ε=−L dI/dt; M from flux linkage

Fast model: Φ = LI or NΦ = MI_other.

LR / RC switching transients

Looks like: Growth/decay I(t)=I₀(1−e^{−t/τ})

Fast model: Find τ=L/R or RC; apply continuity of I_L or V_C.

Method 01 · Phasor triangle

Makes V_L+V_C+V_R ≠ V_source as a feature, not a bug.

Do this: Draw V_R along I; V_L lead I by 90°; V_C lag by 90°; net reactive V_L−V_C.

Method 02 · Resonance limit check

Kills wrong Z(ω) sketches quickly.

Do this: If ω unknown, test ω→0 (C open-ish behaviour) and ω→∞ (L open-ish) for qualitative MC.

Method 03 · Power only on R

Reactive elements store and return energy over a cycle.

Do this: Compute I_rms then P̄=I_rms² R; ignore L and C for average power.

Method 04 · Spectrum ladder

Elementary-use stems are matching, not calculation.

Do this: Memorise order radio→γ and one use each; match wavelength/frequency trends inversely.

Series LCR phasors

Looks like: Z, phase, I₀, resonance

Fast model: Z=√[R²+(X_L−X_C)²]; tanφ=(X_L−X_C)/R.

Power in AC circuits

Looks like: P=V_rms I_rms cosφ; wattless current

Fast model: Average power uses cosφ; ideal L/C average to zero alone.

RC / RL / LC filters qualitatively

Looks like: Lead/lag, high-pass/low-pass behavior

Fast model: Capacitor: current leads V; inductor: current lags.

EM waves basics

Looks like: c=1/√(μ₀ε₀); E/B=c; spectrum order

Fast model: Use relation set; do not invent medium formulas.