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A.P. E&M C * Mega Magnetism Summary I. Hand Rules Cross product AxB = A B sinθ in magnitude and the right hand rule tells its direction. Magnetism in wires; Left hand rules for are electron flow (negative current). Positive charges (and conventional current) obey right hand rules. Straight wires: Loops & Coils: Thumb with current, Fingers with current, fingers curl in the direction thumb points North in the of the B field. direction of the B field. II. Forces on Wires & Charges For wires in B-field Fmagnetic = = I LxB For charges shot through a B-field. qv x B = Fcentripetal = mv2/r Set the above 2 equal to each other to analyze charged particles trapped in circular orbits by magnetic field. III. Calculating B-Fields in Various Situations B = Φ/A B inside long coil = B straight wire = μo I or nμo I B center of a single loop = Magnetic permeability of free space μo = 4π x 10-7 T∙m/A Units: magnetic flux Φ in Webers. Magnetic field strength B in Teslas or Wb/m 2. a. Flux using integration in 2-D b. Gauss' Law for Magnetism (integration in 3-D) c. Biot-Savaart Law: to find any field from any current anywhere d. Ampere's Law IV. Induction Faraday's Law E= B v For moving a wire through a B-field to generate current Lenz's Law E= - n ∆Φ/∆t For moving a magnet in or out of a coil or turning a field on or off IV. AC Circuits L = inductance C = capacitance f= frequency V= voltage I = current R = resistance Z = impedance X = reactance ω = angular frequency Note: oscillating circuits appear on the AP, but they never have an AC Generator in a circuit problem. Material in red on this page will not be on the AP exam, though it is widely taught and appears on the SAT2 in Physics = Summary of the properties of circuit elements. Resistor Capacitor Inductor units symbol relation power dissipated energy stored ohm, Ω = V / A R V=IR P = I V = I² R = V² / R 0 Irms Imax 2 farad, F = C / V C Q=CV henry, H = V s / A L emf = -L (∆I / ∆t) 0 0 PEC = C V² / 2 PEL = L I² / 2 0.707 Imax Inductive reactance XL = 2 f L ω = 2 π f = 1 /√LC Capacitive Reactance Xc = 1/ (2π f C) This AC theory will not be on the AP exam V. RLC Direct Current Circuits Opening and closing circuits: Oscillating RLC Circuits Starting with a capacitor C charged at 1 Volt connected to an inductor L, current grows as capacitor discharges…. …storing magnetic energy in the field ( as the capacitors electric field loses energy ( ½ CV2).