Calculate the required relative permeability of magnetic mat

[D.B0004]

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!

 

[BiGyElLoWhAt]

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?