C32 - Inductance

self-induced emf

ε_L = -L(di/dt)

inductance

L = ε_L/(di/dt) = NΦ_B/i

• 1 H = 1 (kg⋅m²)/(s²⋅A²)

magnetic field energy

U = Li²/2

magnetic field energy density

u_B = B²/2μ₀

mutual inductance

• ε₁ = -M(di₂/dt)

• ε₂ = -M(di₁/dt)

RL circuits

i(t) = (ε/R)(1-e^-t/τ)

i’(t) = (ε/L)e^-t/τ

i(t)_{max → 0} = (ε/R)e^-t/τ = I_maxe^-t/τ

• τ = L/R

LC circuits

• ω = 1/sqrt(LC)

• power & energy identical to original formulas applied to SHM

RLC circuits