formulasheet2

formulasheet2 - Formula Sheet for LSU Physics 2102, Exam 2,...

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Unformatted text preview: Formula Sheet for LSU Physics 2102, Exam 2, Spring ’11 • Constants, definitions: ￿o = 8.85 × 10−12 C2 /Nm2 c = 3.00 × 108 m/s ￿ dipole moment: p = q d ￿ me = 9.11 × 10−31 kg Area of a circle: A = π r 2 v = vo + at x − xo = vo t + 1 at2 2 1 = 8.99 ×109 Nm2 /C2 4π￿o e = 1.60 × 10−19 C Q Q Q charge densities: λ = , σ = , ρ = L A V mp = 1.67 × 10−27 kg Area of a sphere: A = 4π r 2 k= x − xo = 1 (vo + v )t 2 2 v 2 = vo + 2a(x − xo ) µo = 4π × 10−7 T·m/A 1 eV = e(1V) = 1.60×10−19 J g = 9.8 m/s2 Volume of a sphere: V = 4 πr3 3 • Kinematics (constant acceleration) : x − xo = vt − 1 at2 2 ￿ ￿ • Force on a charge in an electric field: F = q E ￿ • Coulomb’s law: |F | = k | q1 || q2 | r2 |q| r2 ￿ • Electric field of a point charge: |E | = k ￿ • Electric field of a dipole on axis, far away from dipole: E = ￿ • Electric field of an infinite line charge: |E | = 2k λ r ￿ • Torque on a dipole in an electric field: ￿ = p × E , τ ￿ ￿ U = −p · E ￿ • Electric flux: Φ = ￿ ￿ ￿ E · dA 2k p ￿ z3 ￿ Potential energy of a dipole in E field: ￿ • Gauss’ law: ￿o ￿ ￿ E · dA = qenc σ 2￿o σ ￿o • Electric field of an infinite non-conducting plane with a charge density σ : E = • Electric field of infinite conducting plane or close to the surface of a conductor: E = • Electric potential, potential energy, and work: ￿f ￿ Vf − Vi = − E · d￿ s In a uniform field: ∆V = −Ed cos θ i ∂V , Ez = − ∂y ∂z n n ￿ ￿ qi q Potential of a point charge q : V = k Potential of n point charges: V = Vi = k r r i=1 i=1 i Electric potential energy: ∆U = q ∆V ∆U = −Wfield q1 q2 Potential energy of two point charges: U12 = Wext = q2 V1 = q1 V2 = k r12 ￿ ￿ E = −￿V, Ex = − ∂x , Ey = − Capacitor with a dielectric: C = κCair Potential Energy in Cap: U = = qV = CV 2C 2 2 ￿ Capacitors in parallel: Ceq = Ci q2 1 1 2 ∂V ∂V • Capacitance: definition: q = CV Parallel plate: C = ε◦ 1 A d ￿ |2 Energy density of electric field: u = κεo |E 2￿ 1 1 Capacitors in series: = Ceq Ci • Current: i = dq dt Current density: J = V i i A Drift speed of the charge carriers: ￿d = v ￿ J ne • Definition of resistance: R = ￿ |E | Definition of resistivity: ρ = ￿ |J | L A Temperature dependence: ρ − ρ◦ = ρ◦ α(T − T◦ ) Power dissipated in a resistor: P = i2 R = V2 R • Resistance in a conducting wire: R = ρ • Power in an electrical device: P = iV • Definition of emf : E = dW dq ￿ Ri • Resistors in series: Req = Resistors in parallel: 1 Req = • Loop rule in DC circuits: the sum of changes in potential across any closed loop of a circuit must be zero. ￿1 Ri • Junction rule in DC circuits: the sum of currents entering any junction must be equal to the sum of currents leaving that junction. • Charging a capacitor, series RC: q (t) = C E (1 − e− τc ), t q (t) = qo e− τc • Magnetic Fields: t time constant τC = RC , Discharging: ￿ ￿ Magnetic force on a charge q: F = q￿ × B v Circular motion in a magnetic field: qv⊥ B = ￿ Magnetic Dipole: µ = N iA ￿ r ￿ ￿ ￿ Magnetic force on a length of wire: F = iL × B 2 mv⊥ ￿ ￿ ￿ Lorentz force: F = q E + q￿ × B v 2π m with period: T = qB Potential energy: U = −µ · B ￿￿ ￿ Torque: ￿ = µ × B τ ￿ T·m ) A • Generating Magnetic Fields: ￿ Biot-Savart Law: dB = 4π (µ0 = 4π × 10−7 r3 µ0 id￿ × ￿ sr µ0 2i 4π r Magnetic field of a circular arc: B = µ0 ia ib 2π d L µ0 i 4π r φ Magnetic field of a long straight wire: B = Force between parallel current carrying wires: Fab = ￿ ￿ Ampere’s law: B · d￿ = µ0 ienc s Magnetic field of a solenoid: B = µ0 in • Induction: ￿ ￿ Magnetic field of a dipole on axis, far away: B = µ0 µ ￿ 2π z 3 Magnetic Flux: Φ = ￿ ￿ B · dA dt (= −N dΦ dt for a coil with N turns) Motional emf: E = BLv Faraday’s law: E = − dΦ ...
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This note was uploaded on 05/20/2011 for the course PHYS 2102 taught by Professor Gimmnaco during the Fall '08 term at LSU.

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