# A b i r example 3 self inductance of a coaxial cable

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a b I r Example 3: Self-Inductance of a coaxial cable Example 3: Self-Inductance of a coaxial cable In thegap (a < r < b): ( 29 a b L r I B ln o o π μ π μ 2 2 = = Show that

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Solution
Kirchhoff’s Loop Rule terms (again) Kirchhoff’s Loop Rule terms (again) - resistor, - capacitor, - inductor, dt dI L V C q V IR V - = = - = I q q I Voltagechangein going along path from left to right: Path direction same as current

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12 V 20mH What is the current 2 ms after the switch is closed? Hint: writedown Kirchoffs loop rule and solvethe differential equation for I Example 4
Energy Energy ε L = - LdI/dt + - How much work is done by an external emf to increase the current from 0 to I final ? I ε 0 dI L dt ε - = Kirchoff’s law gives: (Recall, P=VI) dI I LI dt ε = Power supplied by external emf = power absorbed by inductor

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Power absorbed by inductor is: 2 2 1 LI U L = 2 1 2 f 0 I f L U L I dI LI = = L dU LIdI = Thetotal potential energy stored is: L dU dI LI dt dt = Find thepotential energy of an inductor with L=400mH and a final current of 10A.
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