# Magnetic Core circuit -- Help please

1. Aug 25, 2015

### 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

Where did I do wrong?

2. Aug 25, 2015

### Staff: Mentor

Why do you divide by 700 here?

3. Aug 25, 2015

### 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.

4. Aug 25, 2015

### Staff: Mentor

It is air, μr is 1.

5. Aug 25, 2015

### 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 = Hmean * s , s is the lengt of the whole circulation path.

Bcore = Bairgap , so you can calculate Hairgap , and Hcore = Hairgap/700.

sairgap = 0.1 mm.

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

6. Aug 26, 2015

### c.jinkuan

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

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

7. Aug 26, 2015

### Hesch

It's the length of Lcore + Lairgap.
I suggest that you read Amperes law ( circulation integral ).
B = μ*H , B is constant ( Bairgap = Bcore ) →

μ0*Hairgap = μr0*Hcore

Hcore = Hairgapr

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.

Last edited: Aug 26, 2015
8. Aug 26, 2015

### c.jinkuan

Thanks! Hesch.

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

9. Aug 26, 2015

### Hesch

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 Fm = 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:

Hairgap*Lairgap + Hcore*Lcore = N*I →

Hairgap*Lairgap + ( Hairgapr )*Lcore = N*I

( Hairgap = B / μ0 , B = 0.35T )

Find Lcore.

Last edited: Aug 26, 2015
10. Aug 26, 2015

### rude man

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.