A) The fraction b/a may be written as b/a = (a+b−a) / a = 1 + (( b−a ) / a ). Use the power series expansion ln(1+z)= z + z^(2) / 2+ ⋯) , valid for |z|<1 , to find approximate expression for the inductance when b−a is much less than a. Express your answer in terms of the variables N , I , h , b , a , and appropriate constants. L = ? B) Compare results with this L = μ0*N^(2)*A / 2πr .
A) The fraction b/a may be written as b/a = (a+b−a) / a = 1 + (( b−a ) / a ). Use the power series expansion ln(1+z)= z + z^(2) / 2+ ⋯) , valid for |z|<1 , to find approximate expression for the inductance when b−a is much less than a. Express your answer in terms of the variables N , I , h , b , a , and appropriate constants. L = ? B) Compare results with this L = μ0*N^(2)*A / 2πr .
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A) The fraction b/a may be written as b/a = (a+b−a) / a = 1 + (( b−a ) / a ). Use the power series expansion ln(1+z)= z + z^(2) / 2+ ⋯) , valid for |z|<1 , to find approximate expression for the inductance when b−a is much less than a.
Express your answer in terms of the variables N , I , h , b , a , and appropriate constants.
L = ?
B) Compare results with this L = μ0*N^(2)*A / 2πr .
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