Introduction to General Physics for Technology - Formula Sheet | PHYS 2102, Exams of Physics

Download Introduction to General Physics for Technology - Formula Sheet | PHYS 2102 and more Exams Physics in PDF only on Docsity! PHYS 2102 Formula Sheet Spring 2007. • Constants, definitions: ǫo = 8.85 × 10−12 C2/Nm2 k = 1 4πǫo = 8.99 ×109 Nm2/C2 e = 1.60 × 10−19 C 1 eV = e(1V) = 1.60 ×10−19 J dipole moment: p = qd charge densities: λ = Q L , σ = Q A , ρ = Q V me = 9.11 × 10−31kg mp = 1.67 × 10−27kg Area of a circle: A = πr2 Area of a sphere: A = 4πr2 Volume of a sphere: V = 4 3 πr3 • Kinematics (constant acceleration) : v = v0 + at x − x0 = 12 (v0 + v)t x − x0 = vt − 12at2 x − x0 = v0t + 12at2 v2 = v20 + 2a(x − x0) • Coulomb’s law: F = k | q1 || q2 | r2 • Electric field measured with a test charge: ~E = ~F qo • Force on a charge in an electric field: ~F = q ~E • Electric field of a point charge: E = F qo = k | q | r2 • Electric field of an infinite non-conducting plane with a charge density σ: E = σ 2ǫo • Electric field of an infinite line charge: E = 2kλ r • Electric field of a dipole on axis, far away from dipole: E = 2kp z3 • Torque on a dipole in an electric field: ~τ = ~p × ~E • Potential energy of a dipole in electric field: U = −~p · ~E • Electric flux: Φ = ∫ ~E · d ~A • Gauss’ law: ǫo ∮ ~E · d ~A = qenc • Electric field close to the surface of a conductor: E = σ ǫo • Work, potential energy, and electric potential: ∆U = Uf − Ui = −W ~E = −~▽V, Ex = − ∂V ∂x , Ey = − ∂V ∂y , Ez = − ∂V ∂z U = −W∞ potential of a point charge q: V = k q r V = −W∞ q potential of n point charges: V = n ∑ i=1 Vi = k n ∑ i=1 qi ri Vf − Vi = − ∫ f i ~E · d~s potential energy of two point charges: U12 = Wext = q2V1 = q1V2 = k q1q2 r12 • Kinetic Energy of a particle: K = 1 2 mv2 1 • Capacitance definition: q = CV Capacitor with a dielectric: C = κCair farad = coulomb volt Parallel plate: C = ε◦ A d A d = Area separation Spherical: C = 4πε◦ ab b − a a = inner radius; b = outer radius Isolated sphere: C = 4πε◦R Cylindrical Cap.: C = 2πε◦ L ln(b/a) L = length For a dielectric, substitute κε◦ for ε◦ in the above formulae. κ = dielectric constant Permittivity: ε = κε◦ Potential Energy in Cap: U = q2 2C = 1 2 qV = 1 2 CV 2 Energy density of electric field: u = 1 2 εE2 Capacitors in parallel: Ceq = ∑ Ci Capacitors in series: 1 Ceq = ∑ 1 Ci • Current: i = dq dt In a conductor: i = nqAvd Current density: j = i A • Drift speed of the charge carriers: ~vd = ~J ne • Definition of resistance: R = V i Definition of resistivity: ρ = 1 σ = E J σ = conductivity • Resistance in a conducting wire: R = ρL A • Power in an electrical device: P = iV Power in a resistor: P = i2R = V 2 R • Definition of emf : E = dW dq Rate of change of chemical to electrical energy: Pemf = iE • Resistors in series: Req = ∑ Ri Resistors in parallel: 1 Req = ∑ 1 Ri • Loop rule in DC circuits: the sum of changes in potential across any closed loop of a circuit must be zero. • 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 in a series RC circuit: q(t) = CE(1 − e− tτ ), time constant τ = RC Discharging: q(t) = q0e − t τ , time constant τ = RC • Magnetic Fields Magnetic force on a charge q: ~F = q~v × ~B Lorentz force: ~F = q ~E + q~v × ~B Hall voltage: V = vdBd = i nle B d = width ⊥ to field and i, l = thickness ‖ to field and ⊥ to i Circular motion in a magnetic field: qv⊥B = mv2 ⊥ r so period: T = 1 f = 2πm qB = 2π ω , where f = frequency, ω = angular frequency Magnetic force on a length of wire: ~F = i~L × ~B Definition of a Magnetic Dipole: ~µ = Ni ~A Torque on a Magnetic Dipole: ~τ = ~µ × ~B Energy of a Magnetic Dipole: U = −~µ · ~B 2