chapter30 - Inductance Important fact Magnetic Flux B is...

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1 Important fact: Magnetic Flux Φ B is proportional to the current making the Φ B All our equations for B-fields show that B α I 2 0 ˆ 4 r r l d I B d × = π µ thru I l d B 0 µ = Biot-Savart Ampere Inductance I B B Φ Flux I B Φ Flux Assumes leaving everything else the same. i If we double the current I , we will double the magnetic flux through any surface. Inductance
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2 Self-Inductance (L) of a coil of wire LI B Φ I L B Φ This equation defines self-inductance. Note that since Φ B α I, L must be independent of the current I. L has units [L] = [Tesla meter 2 ]/[Amperes] New unit for inductance = [Henry]. Self-inductance An inductor is just a coil of wire. The Magnetic Flux created by the coil, through the coil itself: = Φ A d B B v v This is quite hard to calculate for a single loop. Earlier we calculated B at the center, but it varies over the area. Inductors (coil of wire)
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3 Consider a simpler case of a solenoid I L N nI B inside 0 0 | | µ µ = = Recall that the B-field inside a solenoid is uniform! N = number of loops L = length of solenoid * Be careful with symbol L ! Inductors I L N nI B inside 0 0 | | µ µ = = = = = Φ A nI N BA N A d B N B ) ( 0 µ L An NnA I L B 2 0 0 µ µ = = Φ = Self-Inductance Length Inductors
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4 Coil 1 Coil 2 I I Inductor 1 consists of a single loop of wire. Inductor 2 is identical to 1 except it has two loops on top of each other. How do the self-inductances of the two loops compare? A) L 2 = 2 L 1 B) L 2 > 2L 1 C) L 2 < 2L 1 Answer: L2 > 2L1 , in fact L2 = 4 L1. The self inductance L increases by 4. L = Φ /i. If we keep i fixed, but double the number N of turns, Φ increases by 4 . Total flux. N doubles, but Φ 1 = BA also doubles because when we double the number of turns, then B is doubled.
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