Ideal Transformer current relationship and problems of B-H relationship

[phwcssin]

When I read the lecture notes about the ideal transformer, I have some problems about the proof of current relationship i1/i2=N2/N1=1/a.The proof is shown below.

Current Relationships of ideal transformer:
To get the current relationships use ampere's law
mmf= ∫H•ds= N1i1+N2i2’
H x length = N1i1+N2i2’
(B x length)/μ = N1i1+N2i2’
Assuming uniform flux density in the core
(φ x length)/( μ x area) = N1i1+N2i2’
If μ is infinite then 0 = N1i1+N2i2’ Hence i1/i2’= -N2/N1 or i1/i2=N2/N1=1/a

Questions:
1.when μ becomes infinity , is B still directly proportional to H here (is B=μH still worked )?

2.If μ becomes infinity then by B=μH as H has some values ,B becomes infinitely large?? μ=∞ ; B=μH=∞? But B will go saturated in reality...It contradicts that B=μH.
If B≠μH then mmf =Hl≠ φ x (l/μS) where l/μS is the reluctance .
Is the reluctance l/μS not suitable for the saturation region of B-H curve?3. I have read the book Power System Analysis by William D. Stevenson (P.45),the author said that B is not infinitely large,therefore integral value of must equal to zero.I don't understand his explanation.Can anyone explain in details to me? Thanks.

Another question: in reality,there is flux leakage around the core ,how can we use the ampere 's circuital law to calculate them?The leakage flux have many path...

 

[Studiot]

Hello, phwcssin and welcome to Physics Forums.

What book did you obtain these formulae from?
Tshey seem a cumbersome way to derive tranformer operation equations.

If the applied voltage is sinusoidal, the flux in the core will be sinsoidal and lags the voltage by one quarter cycle.

However because of the hysteresis curve the magnetising current will not be sinusoidal and cannot be represented by a phasor.