Confusion about the direction of the vectors: motional EMF

Question

I'm working through an example with motional EMF and I'm having trouble understanding the directions of vectors so that I can apply induction law.

The magnetic circuit seems complex because the circuit is used to analyze other situations but the air gap 3, the coil 3 and the single open loop coil are the ones relevant to this. We neglect dispersion and the magnetic reluctance of iron. Section S of the circuit is constant and it's a square of side a. The air gaps have thickness $\delta$. All of the coils have the same number of turns. The open coil has a current $i_0$ that is zero.

Now we have i2=1A and i3=i0=0 which originates a flux $\phi=-1mH$ and $B_3=-0.625 T$.

Now my question is about the next paragraph:

"The motional induction electric field only exists when the coil 0 passes the air gap 3 (I understand that, because only there B is not zero). On that conditions, the elecric field as an orthogonal direction to the figure plan, the same as the current i0 (I think I can also see that...). At the bottom side of the coil we will have $u_0=Bva$ (now that is what I don't understand, what is the direction of B? Is it the same as v? Why? I can't see the direction of the vectors!)."

Basically my question is about the direction of the vectors while applying the induction law. Can someone help me clarify it? I only need a small draw or some brief explanation.

Answer 1

1. B is roughly along the direction of the core, except in the air gaps.
2. B is irrelevant to this problem (!!!), or at least mostly so.
3. A better wording for "when the coil passes the air gap" is "as the coil passes through the air gap". It is the motion of the coil in the air gap that generates a voltage.
4. The reason that the motion of the coil in the air gap generates a voltage is because as the coil moves through the air gap it cuts across the flux $\phi_3$, getting ever less flux as it moves. This is why the B field is made irrelevant -- all you need to know is that the coil is seeing all of $\phi_3$ when it's inside the core, and none when it's outside, and the change must generate some voltage.

You figure out the direction of B along the core using the right-hand rule. Curl the fingers of your right hand in the direction of current flow in the coil, and your thumb points in the direction of B.