How Do I Resolve Discrepancies in Magnetic Circuit Calculations?

[c.jinkuan]

Fm = (500)(10/27)
= 185.185 At
Total flux = βA
= (0.35)(0.003)
= 0.00105 wb
Rm = Fm / total flux
= 185.185 / 0.00105
= 176366.6667 At/wb
R(air) = (0.1 x10^-3) / (700)(4π x 10^-7)(0.003)
= 37.894034 At/wb

Rm = length / μA
length = Rm x μ x A
= (176366.6667 + 37.894034) (700) (4π x 10^-7) (0.003)
= 0.4654206 m

∴ 0.4654206 - (0.1 x10^-3)
= 0.465320 m

My answer is not the same as the answer given in the answer key.
Where did I do wrong?

 

[mfb]

R(air) = (0.1 x10^-3) / (700)(4π x 10^-7)(0.003)

Why do you divide by 700 here?

 

[c.jinkuan]

Rm = length / μA

So,
length = 0.1 x10^-3

μ = (μr) (μo)
= (700)(4π x 10^-7)

A = 0.003

I followed the formulas given to me.

 

[mfb]

It is air, μr is 1.

 

[Hesch]

#1: You cannot use the cross section area to anything because it's the flux density that is given ( not the flux ).

So N*I = 185.185A = H_mean * s , s is the lengt of the whole circulation path.

B_core = B_airgap , so you can calculate H_airgap , and H_core = H_airgap/700.

s_airgap = 0.1 mm.

Now use a kind of a magnetic version of Kirchhoffs voltage law to create an equation to find s_core.

 

[c.jinkuan]

s is the lengt of the whole circulation path.

What do you mean by the length of the circulation path?
And why H_core = H_airgap / 700 ?

Sorry I still don't understand, and I am getting confused with the formula.

 

[Hesch]

What do you mean by the length of the circulation path?

It's the length of L_core + L_airgap.
I suggest that you read Amperes law ( circulation integral ).

And why H_core = H_airgap / 700 ?

B = μ*H , B is constant ( B_airgap = B_core ) →

μ₀*H_airgap = μ_r*μ₀*H_core →

H_core = H_airgap/μ_r

B is constant because it's the same flux that passes anywhere in the circuit, and there is no change in the cross section area in the circuit.

 

[c.jinkuan]

Thanks! Hesch.

I have one question.
The magnetomotive force (F_m) produced from the coil is for the core and the air gap or just for the core only?

 

[Hesch]

The magnetomotive force (F_m) produced from the coil is for the core and the air gap or just for the core only?

I don't know. I regard it different:
Magnetic fields are circular fields. They bite themselves in the tail. Along a circular path you cannot say "here it is" and "here it is not".
You could say that this F_m = N*I.
Also you could say that

N*I - ∫_circulationH⋅ds = 0 ( according to Kirchhoffs 2. law mentioned in #7 ( analogy ) ).

When using Amperes law, of course you will sketch a circulation path through the middle of the core and middle of the airgap. Then you could write an equation:

H_airgap*L_airgap + H_core*L_core = N*I →

H_airgap*L_airgap + ( H_airgap/μ_r )*L_core = N*I

( H_airgap = B / μ₀ , B = 0.35T )

Find L_core.

 

[rude man]

Thanks! Hesch.

I have one question.
The magnetomotive force (F_m) produced from the coil is for the core and the air gap or just for the core only?

mmf is around the entire mag circuit. Like emf is around an electric circuit. So mmf includes everything in the closed mag circuit.
mmf = ∑ΦR around the mag. circuit like emf = ΣiR around an electric circuit.