AP Physics C: E&M Unit 13 Cheatsheet: Electromagnetic Induction

Magnetic flux measures how much magnetic field passes through a surface.

For uniform field:

Φ_B = B · A = BA cos θ

• θ = angle between B and area vector
• Area vector: perpendicular to surface, outward from closed surfaces
• Units: Weber (Wb) = T·m²

For non-uniform field:

Φ_B = ∫ B · dA

Sign convention: Dot product determines sign. Flux is positive when B points outward; negative when inward.

LC circuit: Charged capacitor + inductor, no resistance.

Energy conservation:

U_C + U_L = constant

q²/(2C) + ½LI² = constant

Charge oscillates as SHM:

d²q/dt² = −q/(LC)

Angular frequency:

ω = 1/√(LC)

Period: T = 2π√(LC)

Maximum current: Use energy conservation at t = 0 (all energy in capacitor):

I_max = Q₀/√(LC) = Q₀ω

where Q₀ = initial charge on capacitor.

Flux & Faraday problems:

1. Identify what changes: B, A, or angle θ
2. Write Φ_B = BA cos θ or use integral
3. Differentiate with respect to time
4. Apply ε = −dΦ_B/dt; include negative sign
5. Use Lenz's law to verify direction

LR circuit problems:

1. Write Kirchhoff equation: ε = L(dI/dt) + IR
2. Identify initial condition (I at t = 0)
3. Solve exponential: I(t) = I_∞ + (I₀ − I_∞)e^−t/τ
4. Calculate τ = L/R

LC circuit problems:

1. Use energy conservation to find I_max
2. Find ω = 1/√(LC)
3. Write q(t) and I(t) as sinusoidal functions