Formula Sheet for General Physics for Technical Students | PHYS 2102, Study notes of Physics

Download Formula Sheet for General Physics for Technical Students | PHYS 2102 and more Study notes Physics in PDF only on Docsity! PHYS 2102 Formula Sheet Spring 2009. • Constants, definitions: ǫo = 8.85 × 10−12 C2/Nm2 k = 1 4πǫo = 8.99 ×109 Nm2/C2 µ0 = 4π × 10−7 T·mA c = 3.00 ×108 m/s e = 1.60 × 10−19 C 1 eV = e(1V) = 1.60 ×10−19 J dipole moment: ~p = q~d charge densities: λ = Q L , σ = Q A , ρ = Q V me = 9.11 × 10−31kg mp = 1.67 × 10−27kg gravity g = 9.81 m/s2 Area of circle: A = πr2 Area of sphere: A = 4πr2 Volume of 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 • Force on a charge in an electric field: ~F = q ~E • Electric field of a point charge: E = k | q | r2 • Electric field of a dipole on axis, far away from dipole: E = 2kp z3 • Electric field of an infinite line charge: E = 2kλ r • 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 of an infinite non-conducting plane with charge density σ: E = σ 2ǫo • Electric field of infinite conducting plane, or close to the surface of a conductor: E = σ ǫo • Electric potential, potential energy, and work: Vf − Vi = − ∫ f i ~E · d~s, In a uniform field: ∆V = −Ed cos θ ~E = −~▽V, Ex = − ∂V ∂x , Ey = − ∂V ∂y , Ez = − ∂V ∂z Potential of a point charge q: V = k q r Potential of n point charges: V = n ∑ i=1 Vi = k n ∑ i=1 qi ri Electric potential energy: ∆U = q∆V ∆U = −Wfield Potential energy of two point charges: U12 = Wext = q2V1 = q1V2 = k q1q2 r12 1 • Capacitance definition: q = CV Capacitor with a dielectric: C = κCair Parallel plate: C = ε◦ A d Potential Energy in Cap: U = q2 2C = 1 2 qV = 1 2 CV 2 Energy density of electric field: u = 1 2 κε0E 2 Capacitors in parallel: Ceq = ∑ Ci Capacitors in series: 1 Ceq = ∑ 1 Ci • Current: i = dq dt Current density: J = i A • Drift speed of the charge carriers: ~vd = ~J ne • Definition of resistance: R = V i Definition of resistivity: ρ = E J • 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 • 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−t/τC), time constant τC = RC Discharging: q(t) = q0e −t/τ • Magnetic Fields Magnetic force on a charge q: ~F = q~v × ~B Lorentz force: ~F = q ~E + q~v × ~B Circular motion in a magnetic field: qvB = mv2 r with period: T = 2πm qB Magnetic force on a length of wire: ~F = i~L × ~B Magnetic Dipole: ~µ = Ni ~A Torque on a Magnetic Dipole: ~τ = ~µ × ~B Energy of a Magnetic Dipole: U = −~µ · ~B 2