In the approximately ideal magnetizable iron circle with two different air gaps two coils are arranged concentrically. Calculate the mutual inductance without regard to the scattering.
I have results but I don't understand some parts so if someone would like to help me, I would be thankful.
First they use Ampere's law:
\(B_1\delta _1+B_2\delta _2=\mu_0N_1I_1\)
I don't understand this at all, why this sum, why those formulas?
Than Gauss's law:
\(\Phi =B_1A_1=B_2A_S\)
I understand this part.
And than they use:
\(\Phi_{v2} = -\Phi N_2\)
From where comes this minus?

I have results but I don't understand some parts so if someone would like to help me, I would be thankful.
First they use Ampere's law:
\(B_1\delta _1+B_2\delta _2=\mu_0N_1I_1\)
I don't understand this at all, why this sum, why those formulas?
Than Gauss's law:
\(\Phi =B_1A_1=B_2A_S\)
I understand this part.
And than they use:
\(\Phi_{v2} = -\Phi N_2\)
From where comes this minus?