Physics Constants and Formulas: Electricity and Magnetism - Prof. Darin E. Acosta, Study notes of Physics

Download Physics Constants and Formulas: Electricity and Magnetism - Prof. Darin E. Acosta and more Study notes Physics in PDF only on Docsity! Constants: e = 1.6 × 10−19 C mp = 1.67 × 10−27 kg me = 9.1 × 10−31kg ǫo = 8.85 × 10−12 C2/N · m2 1/(4πǫo) = 9 × 109 N · m2/C2 µo = 4π × 10−7T · m/A c = 3 × 108m/s nano = 10−9 micro = 10−6 Coulomb’s Law: |~F | = |q1||q2| 4πǫor2 (point charge) Electric field: ~E = ~F q ~E = q 4πǫor2 r̂ (point charge) ~E = ∫ dq 4πǫor2 r̂ (general) Gauss’ law: ΦE = n̂ · ~E A = ∮ n̂ · ~E dA = qenc ǫo Energy: W = ∫ ~F · d~s = 1 2 mv2f − 1 2 mv2i = Kf − Ki For conservative forces Uf − Ui = − ∫ ~F · d~s → Ki + Ui = Kf + Uf Electric potential: V = U q V = q 4πǫor (point charge) V = ∫ dq 4πǫor (general) Vb − Va = − ∫ b a Exdx = − ∫ b a ~E · d~s Ex = − ∂V ∂x , Ey = − ∂V ∂y , Ez = − ∂V ∂z Capacitors: q = CV C = ǫoA d (parallel-plate) C = C1 + C2 (parallel) UE = q2 2C uE = 1 2 ǫoE 2 1 C = 1 C1 + 1 C2 (series) Resistors: i = dq dt = jA R = V i R = ρL A (wire) P = iV R = R1 + R2 (series) 1 R = 1 R1 + 1 R2 (parallel) τRC = RC Magnetism: ~F = q~v × ~B ~F = i~L × ~B µ = NiA ~τ = ~µ × ~B U = −~µ · ~B d~B = µo 4π id~s × r̂ r2 ∮ ~B · d~s = µoienc B = µoi 2πR (wire), µoi 2R (loop center), µoiN L (solenoid) Induction: ΦB = n̂ · ~B A = ∮ n̂ · ~B dA E = ∮ ~E · d~s = −dΦB dt L = NΦB/i (definition) L = µon 2Al (solenoid) E = −Ldi dt E1 = −M di2 dt UB = 1 2 Li2 uB = B2 2µo i = ioe −t/τL τL = L/R Vs Vp = Ns Np AC Circuits: ω = 1√ LC (LC circuit) E = Em sin(ωt) i = I sin(ωt − φ) (driven RLC) I = Em Z tan φ = ωL − 1ωC R Z = √ R2 + (ωL − 1 ωC )2 vL = L di dt vC = q C Pavg = 1 2 IEm cosφ Maxwell’s Eqs.: ∮ ~B · n̂dA = 0 ∮ ~B · d~s = µoǫo dΦE dt + µoienc id = ǫo dΦE dt EM Waves: c = E B = 1√ µoǫo ~S = 1 µo ~E × ~B I = Savg = 1 cµo E2rms Erms = Em√ 2 I = Ps 4πr2 I = Io cos 2 θ n1 sin θ1 = n2 sin θ2 θc = sin −1 n2 n1 θB = tan −1 n2 n1 pr = I c (absorp.), 2I c (refl.)