Chapter 30 lecture - Chapter 30 Inductance M and L Begin Ch...

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Chapter 30 Inductance M and L Begin Ch 30 today Tuesday: RL, LC, LRC circuits
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Mutual Inductance changing i 1 1 21 2 21 21 2 1 21 1 2 21 21 1 21 2 21 2 2 : , : i N M giving dt d N dt di M have also we but dt di M definition l operationa M dt di M and dt d N induced Φ = Φ = - = - = Φ - = ξ Induced ξ 2 Current changing in coil 1 produces a changing B field and hence changing flux Φ 21 through coil 2. By Faraday’s law there is an induced emf ξ 2 in coil 2 at/thru 2 due to 1 DEMO Ф 21
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How does M 12 relate to M 21 ? (change current in coil 2 and measure induced ξ 1 ) ) ! ... ?? ( between) nce ze2)(dista (size1)(si ize2)] between)(s stance (size1)(di [ 12 21 2 1 21 1 1 1 2 1 21 2 21 true and plausible M M N N M i i N N i N M = = = Φ = Thus we can drop subscripts on M 2 12 1 1 21 2 2 1 1 2 : i N i N M or dt di dt di M Φ = Φ = - = - = ξ Units of inductance: Henry, H H = Tm 2 /A = Wb/A
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Uses of Mutual Inductance Question 1: Nested Solenoids: consider a smaller diameter solenoid (with N 2 and area A 2 ) inside a larger diameter solenoid (with N 1 and area A 1 ) of the same length, L. Which parameter does NOT appear in M? A 1 L A 2 1 1. A 1 2. A 2 3. N 1 4. N 2 L A N N i A B N i N M 2 1 0 2 1 2 1 2 1 21 2 μ = = Φ =
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Self Inductance, L Consider a long solenoid hooked to a battery. When S is closed does I jump instantly to V/R? Energy considerations suggest no as I increases so does B through each loop generating an emf in each loop of –dΦ/dt (opposing increase). For all N loops in the solenoid there is a total opposing emf of: i N L and dt di L general in then dt di L dt di L A N dt di L N NA dt dB NA dt d N sol sol sol Φ = - = - = - = - = - = Φ - = ξ μ : ) ( 2 0 0 Same for Toroid (ex 30.3) L goes to 2πr Calculation of L, like M may be difficult
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Question 2 Suppose I know the inductance L 1 of a single loop of wire. If I hook up N of these isolated loops in series, but widely separated, what is the total inductance of these N loops?
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Chapter 30 lecture - Chapter 30 Inductance M and L Begin Ch...

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