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?