Ch28-31sheet - Ch 28 Biot-Savart B = inside B = 0 I r 2R R...

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Ch. 28 Biot-Savart: B = μ 0 4 π Idl × r r 2 outside straight conductor: B = μ 0 I/ (2 πx ) inside: B = μ 0 I 2 πR r R parallel conds: F/L = μ 0 I 1 I 2 / (2 πr ) B at center of circular current loop: B = μ 0 NI/ (2 a ) for N loops Ampere’s Law: B · dl = μ 0 I encl = μ 0 j · dA inside solenoid: B = μ 0 nI (n: turns/length) B toroid = μ 0 NI 2 πr Ch. 29 motional emf: Δ V = vBL Faraday’s Law: V loop = - d Φ B dt = - d dt surf B · dA Changing B, no motion: V loop = - N dB dt A for N loops Lenz’s Law: induced currents produce flux to oppose the original change in Φ B induced E field: E = 1 2 πr d Φ dt AC generator: Φ B = NB · A = NBA cos( ωt ) V = - d Φ B dt = NBAω sin( ωt ) mag dipole of orbiting particle: μ = evr 2 = e 2 m L (L = ang. mom.) mag materials: B inside = B 0 + μ 0 M , where mag- netism M = μ tot /V B inside = K m B 0 = (1+ χ m ) B 0 ( K m : relative perme- ability (near 1), χ m : mag susceptibility) χ m : dia = - 10 - 5 , para = 10 - 5 to 10 - 3 , ferro below Curie temp = 100 to 100000 displacement I: B · dl = μ 0 ( I C + I D ) = μ 0 J C + J D · dA where J C = 1 ρ E wire and J D = 0 dE cap dt so B · dl = μ 0 ( I c + 0 d Φ E dt ) c = 1 μ 0 0 Ch. 30 mutual inductance: N 2 Φ 21 i 1 = N 1 Φ 12 i 2 (remember Φ 21 = B 1 A 2 ) self-inductance (solenoid and toroid): L sol = μ 0 N 2 A L . Also, L = - V di/dt = N Φ i inductor in a circuit: Δ V = - L di dt , U = 1 2 LI 2 U sol = 1 2 Al μ 0 B 2 density u B = U sol Al = B 2 2 μ 0 LR buildup: i = V R (1 - e - t/τ L ), τ L = L/R LR decay: i = i 0 e - t/τ L ; U ( t ) =
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