Physics Cheat sheet (magnetic fields)

# Physics Cheat sheet (magnetic fields) - The Magnetic Field...

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Physics Cheat Sheet for Chapter 30-32 The Magnetic Field: F qv B B = × The SI unit for B is the tesla (T): 1 T = 1 N/(A*m) = 10^4 gauss. F qE E = F qvB B = sin φ E F q = A Circulating Charge: qvB m v r = 2 r mv qB = (radius) T r v v mv qB m qB = = = 2 2 2 π π π (period) f T qB m = = 1 2 π (frequency) a v R = 2 (circular orbit) The Magnetic Force on a Current-Carrying Wire: F iL B B = × dF idL B B = × Torque on a Current Loop: τ μ = × B τ μ θ = B sin μ = NiA The Biot-Savart Law: ( 29 dB o ids r r = × μ π 4 3 (Biot-Savart law) μ π o T m A T m A = × × - - 4 10 126 10 7 6 / . / (Permeability Constant) A Long Straight Wire: B o i r = μ π 2 B o i R = μ 4 (semicircle) The Force Between Parallel Wires: F i LB ba b a Li i d o a b = = μ π 2 Ampere’s Law: B ds i o = μ (need symmetry to calculate h B ) A Solenoid and a Toroid: B i n o o = μ (ideal solenoid) B o o i N rr = μ π 2 (toroid) Field of a Magnetic Dipole: ( 29 B z o rz = μ μ π 2 3 ( μ being the dipole moment of the loop) Definition of Magnetic Flux: Φ B B dA = Faraday’s Law of Induction: ε = - = d
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