What is the length of the inductor?

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SUMMARY

The discussion centers on calculating the length of a 0.5533 mH inductor, which has a length that is four times its diameter. The user attempted to solve the problem using the formula L = (μ₀ * π * r² * N²) / l, substituting the diameter incorrectly as half the radius. The correct relationship is established as length = 4 * diameter, leading to the conclusion that the diameter should be calculated as 2 * radius. The user initially calculated the length as 0.61831 meters, which was incorrect due to the misunderstanding of the diameter and radius relationship.

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  • Understanding of inductor properties and formulas
  • Familiarity with the concept of inductance (L)
  • Knowledge of unit conversions (cm to m)
  • Basic geometry related to circles (radius and diameter)
NEXT STEPS
  • Review the formula for inductance in detail, specifically L = (μ₀ * π * r² * N²) / l
  • Study the relationship between diameter and radius in cylindrical objects
  • Practice unit conversions, particularly from centimeters to meters
  • Explore additional examples of inductor calculations to reinforce understanding
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Homework Statement


A 0.5533 mH inductor has a length that is
four times its diameter.
If it is wound with 15.4 cm−1 turns per
centimeter, what is its length? Answer in
units of m.


Homework Equations



L= (Uo*pi*r^2*N^2)/(l)
N= n*l
length=4*diameter therefore l= 2*r

The Attempt at a Solution



so i substituted them back in the first equation
length^3= (L*4)/(Uo*pi*n^2)

after solving for length i got 0.61831 meters .. and it turns to be wrong !

i need your help

i have changed the units from cm^-1 to meters^-1


need your help thanks a lot
 
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length=4*diameter therefore l= 2*r

Well, there is a problem with this part. The diameter is 2*radius. What you have done is used diameter = 0.5*radius.
 

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