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329lect15 - 15 Inductance — solenoid shorted coax •...

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Unformatted text preview: 15 Inductance — solenoid, shorted coax • Given a current conducting path C , the magnetic flux Ψ linking C can be expressed as a function of current I circulating around C . Ψ I I, E =- L dI dt V ( t ) = L dI dt + - 3 2 1 1 2 3 3 2 1 1 2 3 x z • If the function is linear, i.e., if we have a linear flux-current relation Ψ = LI, then constant L is termed the self-inductance 1 of path C . – Differentiating this relation with respect to time t , and using the fact that E =- d Ψ dt , we find that the emf of an inductor L is simply E =- L dI dt , which is a voltage rise across the inductor in the direction of cur- rent I (which, of course makes L dI dt a voltage drop in the same direction as used in circuit courses). – If emf E is measured around an n-loop coil, then n Ψ = LI defines the inductance L . 1 A mutual inductance M 12 , by contrast, relates the flux linking coil C 2 to a current I 1 flowing in a second coil C 1 . 1 Inductance of long solenoid: Consider a long solenoid carrying a current I and having a density of N loops per unit length as examined in Example 3 of Lecture 12 (see figure in the margin). As determined in Example 3, the3 of Lecture 12 (see figure in the margin)....
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329lect15 - 15 Inductance — solenoid shorted coax •...

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