# Induction in transformer coil relationship to magnetic field lines in core

From my understanding is the process of induction described by a magnetic field line which approaches a wire perpendicular and creating an local electric field in it which can be detected which measuring electrical voltage at the ends of the wire.

What bothers me is this process in a secondary transfer coil. The magnetic field lines are inside the core and do not cut the coil wire at the surface of the core.

Does one need to differentiate between induction by magentic field lines cutting a wire perpendicular and the sum of magentic field lines inside a loop of wire? How exactly does induction happen in the last case compared to the first case?

From my understanding is the process of induction described by a magnetic field line which approaches a wire perpendicular

That is the wrong idea. This is the right idea: -

Does one need to differentiate between induction by magentic field lines cutting a wire perpendicular and the sum of magentic field lines inside a loop of wire?

Induction is not due to lines of flux cutting the wire perpendicularly. If you are talking about this scenario: -

Then it is incidental that some magnetic flux lines are passing through the conductor.

• So you mean that even in the last picture I have the so called necessary (one) loop of wire? So it is always about change of lines of flux over an area A in a closed loop of wire. Commented Jun 14, 2018 at 10:10
• @hendrik2k1 It does boil down to that. However, if the north and south poles were vertically very high and fully enclosed the loop, there would be no measured induced voltage with motion because there is no net change of flux with motion. Commented Jun 14, 2018 at 10:27
• you mean when the loop radius is big and the area of my permanent magnet small in comaprison. When moving this inside the loop the net sum of lines of flux would not change and so I would register no voltage? Commented Jun 14, 2018 at 12:32
• No, that isn't what I said. Commented Jun 14, 2018 at 12:35
• The magnet poles are much bigger in area than the coil loop area. Commented Jun 19, 2018 at 8:37

The fundamental thing is how much flux is contained within a closed loop of wire. When that flux changes, a voltage is induced in the closed loop. It doesn't matter what material is within the loop, whether air, ferrite, iron or whatever.

There are two ways to change the flux within the loop. One is to change the strength of the flux, as in a transformer. Second, the loop can move with respect to the field, resulting in the wire of the loop 'cutting' lines of field, as in a motor or generator.

• But is a closed loop necessary? When I only have a straight wire of say 1 meter and pulling the magnet over it in the middle I would not expect this to be a closed loop of wire. Commented Jun 14, 2018 at 9:17
• there is always a loop - the connections eventually must loop back somewhere Commented Jun 14, 2018 at 11:34

In my opinion, the math obscures the behavior. As you've noted, the induced voltages are orthogonal to the "magnetic flux", so how does this happen?

Relativistically, [ahh the spell checker does not like that word], when the Lorentzian compression maths are developed for masses and accelerations and momentums, some orthogonal forces show up.