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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 4πo 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 2o 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.
- Fall '08