Calculate the required relative permeability of magnetic mat

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SUMMARY

The discussion focuses on calculating the required relative permeability (μr) of a magnetic material for a coil with an inductance of 23.6μH, a maximum current of 4A, and a flux density limit of 1.3T. Participants emphasize the need to first determine the number of turns (N) on the core, which is essential for deriving μr using the equations provided. Key equations include Lm = N^2/R and Bm = μm*N^2/lm. The challenge lies in finding N, which is critical for solving the problem accurately.

PREREQUISITES
  • Understanding of inductance calculations using Lm = N^2/R
  • Familiarity with magnetic flux density and its relation to current
  • Knowledge of core dimensions and their impact on magnetic properties
  • Proficiency in using equations related to magnetic circuits
NEXT STEPS
  • Calculate the number of turns (N) required for the coil based on given parameters
  • Explore the relationship between maximum current and maximum flux in magnetic circuits
  • Study the effects of flux density on magnetic material selection
  • Review the equations in "Electric Machines and Drives" by Ned Mohan for additional insights
USEFUL FOR

Electrical engineering students, hobbyists designing inductive components, and professionals involved in magnetic material selection for coil applications.

D.B0004
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Homework Statement


Consider the core of dimensions given in example 5-1. A coil requires an inductance of 23.6μH, a maximum current of 4A is allowed, and flux density is not to exceed 1.3T. Calculate the required relative permeability, μr, of the magnetic material that should be used.

(HINT: You will need to consider N, the number of turns on the core. Compute this first, and use the result to find µr)

Homework Equations


Lm = N^2/R
Bm = μm*N^2/lm
gamma = N*PHI
PHI = N*i/Rm
PHIm = Bm*Am

The Attempt at a Solution


I can solve the solution IF I can solve for N, the number of turns in the core. I cannot find a way to do this. Can anyone point me in the right direction? Am I missing an equation? I've read thru class notes and our book (Electric Machines and Drives - Ned Mohan) and cannot find something that would lead to N. Thanks!
 
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Hmmm... perhaps there's something to this flux density? You're presumably given the dimensions of the coils in the figure (which you didn't post for some reason). You also know the maximum current. The maximum current is related to the maximum flux, no? How do they relate?
 

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