P31_080 - L toroid l ≈ µ N 2 A l 2 = µ n 2 A which indeed reduces to that of a long solenoid Note that the approximation ln(1 x ≈ x is used

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80. If the solenoid is long and thin, then when it is bent into a toroid ( b a ) /a is much less than 1. Therefore, L toroid = µ 0 N 2 h 2 π ln µ b a = µ 0 N 2 h 2 π ln µ 1+ b a b µ 0 N 2 h ( b a ) 2 πb . Since A = h ( b a ) is the cross-sectional area and l =2 πb is the length of the toroid, we may rewrite this expression for the toroid self-inductance as
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Unformatted text preview: L toroid l ≈ µ N 2 A l 2 = µ n 2 A , which indeed reduces to that of a long solenoid. Note that the approximation ln(1 + x ) ≈ x is used for very small | x | ....
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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