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PHYSICS 208 EXAM II Formula/Information Sheet • Basic constants: Gravitational acceleration on Earth’s surface Permittivity of free space Permeability of free space Elementary charge Unit of energy: electron volt Unit of energy: kilowatt-hour • Properties of some particles: • Some indefinite integrals: g 0 µ0 e 1 eV 1 kWh Particle Proton Electron Neutron R R R dx x dx (x2 +a2 )3/2 √ dx x2 ±a2 = = ln x √x = ln (x + a2 = = = = = = 9.8 m/sec2 8.8542 × 10−12 C2 /N·m2 [ k = 1/4π0 = 8.9875 × 109 N·m2 /C2 ] 4π × 10−7 T·m/A [ km = µ0 /4π = 10−7 Wb/A·m] 1.60 × 10−19 C 1.60 × 10−19 J 3.6 × 106 J Mass [kg] 1.67 × 10−27 9.11 × 10−31 1.67 × 10−27 Charge [C] +1.60 × 10−19 −1.60 × 10−19 0 R R 2 x2 +a √ x2 ± a2 ) R dx a+bx x dx (x2 +a2 )3/2 √x dx 1 b = = ln (a + bx) − √ 21 2 √ x +a x2 ± a2 = x2 ±a2 |q1 q2 | |~r2 − ~r1 |2 q k 2 R̂ R X X kqi ~i = E R̂i 2 Z Z Ri kdq ~i = R̂ dE R2 Coulomb’s law (q at ~r1 , q0 at ~r2 ) |F~ | = Electric field [N/C = V/m] ~ ≡ ~r0 − ~r) (q at ~r0 , observer at ~r, R ~ r) E(~ = (group of charges) ~ E = (continuous charge distribution) ~ E = ~ (on q subject to E) ~ |E| ~ |E| F~ = 2k|λ| r = 2πk|σ| = line charge λ sheet charge σ Electric force [N] Electric flux Gauss’ law (small area ∆Ai , outward normal n̂i ) ∆ΦE = (through an entire surface area) ΦE = (through a closed surface area) ΦE ≡ ~ · n̂)out (E = Conductor Electric potential [Volt = J/C] Electric potential energy [J] (definition, step-length ds along ŝ) ∆V ~ qE ~ i · n̂i ∆Ai = Ei ∆Ai cos θi E Z Z X ~ · n̂dA E lim ∆ΦE = dΦE = ∆A→0 I I dΦE = ~ · n̂dA = 4πkQenc E 4πkσS = Z Z B VB − VA = ∆V V (~r) = = ~ i ≡ ~r − ~ri ) (group of charges, R V (~r) = (continuous charge distribution) V (~r) = ∆U = Z ~ i |) = Vi (|R Z dV = X kqi kdq ~ |R| ~ i| |R ~ E U12 = = = (V (∞) = 0) (V (∞) = 0) Z B ~ · ŝds E UB − UA = −q0 A ~ from V E Electric potential energy of two-charge system ~ · ŝds E A ~ · (~rB − ~rA ) −E q k (V (∞) = 0) ~ |R| X B dV = − A ~ = constant) (E (point charge q at ~r0 ) (definition) k q0 (VB − VA ) ~ ~ = gradient operator) −∇V (∇ q1 q2 k |~r1 − ~r2 | Capacitance [Farad = C/V] Sphere of radius R Parallel plates of area A and separation d Effect of dielectric on electric field (definition) Electrostatic potential energy [J] stored in capacitance Electric energy per unit volume Electric dipole moment (2a = separation between two charges) Torque on electric dipole moment Potential energy of an electric dipole moment Current [A] (definition) with motion of charges Current density [A/m2 ] Resistivity [Ω·m] Resistance [Ω] Current provided by Emf E [V] Power provided by emf E [J/s] Energy loss rate by R [J/s] Time constant in RC circuit [s] (definition) for uniform cross-sectional area A internal resistance r Magnetic force [N] Magnetic field [N] Magnetic moment [A·m2 or J/T] Torque [N·m] Energy [N·m] sheet charge σm = qm /A Q = ∆V = R k A = 4πkd = E0 /κ 1 Q(t)2 UE (t) = 2 C uelectric = 0 E 2 /2 = E 2 /8πk |~ p| = 2aq ~ ~τ = ~ p×E ~ U = −~ p·E C C C E I I J ρ R R I P P τRC on pole qm due to pole Qm poles ±qm separated by l on a magnet of a magnet ≡ = = = ≡ = = = = = F~ ~ |B| |~ µ| ~τ U ~ |B| d Q(t) dt nqvd A R I (where I = J~ · n̂ dA) A ~| |E ~ |J| ∆V I ρ A` (E − ∆V )/r EI I 2 R = (∆V )2 /R = I(∆V ) RC ~ = qm B = kmR|Q2 m | = qm l ~ =~ µ×B ~ = −~ µ·B = 2πkm |σm |