# Magnetic Flux inside a Transformer

1. May 18, 2012

### nemesiswes

I have read that when the secondary of a transformer has current flow, it will reduce the magnetic flux in the core. This then reduces the back-emf on the primary, causing a increase in current to reestablish the magnetic flux to what it once was.

What I want to know is when the secondary produces enough counter flux to decrease the flux in the core to 0, isn't there still magnetic flux in the core? Because the primary creates its own magnetic flux and so does the secondary (even if only briefly because of speed of light delays), they are just opposing each other. It is just like two electromagnets opposing each other. it's like they would each have a little bubble around themselves, except concentrated within the core, lol.

The Other question is if the flux in the core is 0 than will the Primary still be able to induce a voltage on the secondary? Normally you would think no because there is no flux for a rate of change to move back through. But if the primary and secondary each still have there own magnetic flux, equally opposing in strength, then a change in the primary's magnetic flux could still move back through the primary's flux and then through the secondary's magnetic flux to still induce a voltage.

An analogy could be two bubbles, both are pushing against each other (not popping or combining) and a vibration in one bubble will propagate through the one and into the other bubble. Obviously once the Primary stops changing then no voltage can be induced on the secondary anymore, just like the bubbles, no vibration in one means there can be no vibration in the other(there can but let's say the only possible vibration it could ever have was the one you caused, lol).

2. May 19, 2012

### Jano L.

This is not accurate wording. The magnetic flux in the core is meant to denote the product of the magnetic field B and the cross section of the core S. Since the core contains the flux, you are right that this flux is constant throughout the core and is the same in both primary and secondary part of it.

The transformer serves to generate different induced em voltage (emf) along the secondary wiring, but not by decreasing the flux in the core, but by decreasing the flux through the secondary coil. This is a different thing. It is proportional to the number of turns of wire that are penetrated by the magnetic lines. If the number of turns of the secondary is $N_2$,the flux through the coil is $N_2 BS$ and the emf on the poles of the secondary is

$$U_2 = N_2 d(BS)/dt.$$

3. May 19, 2012

### nemesiswes

First, I think it might be easier to think of this as a air core transformer.

Well I was trying to think of this from very small time scales, like picoseconds or nano seconds. Basically where a change in the primary or secondary has not yet reached back to the other coil. What I meant was what happens when the secondary coil is equal in strength to the primary? Since the two magnetic fluxes should cancel, would the primary still be able to induce a voltage on the secondary? I am talking about the small time scale where the secondary finally reaches unity with the primary's magnetic flux strength. in this very short time before the primary increases current pull to compensate for this, will it still be able to induce a voltage on the secondary?

If it can't then wouldn't you be able to see tiny oscillations in the secondary of the transformer because the secondary would reach unity and voltage would drop, then a short time later, the primary increases current, increasing the magnetic flux and the secondary would see another voltage induced, thus causing a increase in current flow on the secondary until it's magnetic flux reaches unity again and then the process repeats.

or would the primary be able to induce a voltage on the secondary no matter what the magnetic flux strength was from the secondary. Like two bubbles, one could br the size of the earth (larger magnetic flux, secondary coil) and the other the size of a atom (smaller magnetic flux , primary coil), still even here the smaller bubble could still create vibrations in the larger bubble (rate of change, voltage induced).

Or another way to think of it, If the secondary is shorted with a 200 watt DC source and the primary is powered by a 10 watt AC source, can the primary still induce a voltage on the secondary? Since the secondary is obviously creating a much larger magnetic flux in the core, could the primary still induce a voltage. If you think of it like the bubble's , then I think it would still be able to induce a voltage on the secondary.

So yeah pretty simple question, when the secondary is at unity with the Primary in terms of magnetic flux strength, does the Primary still induce a voltage?

4. May 20, 2012

### Jano L.

I am sorry, I misunderstood your question.

I will refer to this part:
"voltage" is not a good word in this situation. There is no electrostatic potential if you have AC current nearby.

I think what you are interested in, is

can the primary exert an influence on the current in the secondary?

We can understand the current in the secondary as caused by two independent effects:

1) one is the electrostatic electric field $\mathbf E_{bat}$ induced by DC battery with emf $U_{bat}$
2) the second is the vortical electric field $\mathbf E_{dyn}$ due to alternating current in both primary and secondary coil. This field is caused by letting the AC flow through the primary.

The sum effect of the two forces is that the current $I_2$ in the secondary coil is given by

$$I_2 = \frac{U_{bat} + U_{dyn}}{R},$$

where
$$U_{dyn} =- M\dot I_1 - L_2 \dot I_2$$

is the emf of the vortical field(signs could be wrong). $M$ is mutual inductance and $L_2$ is the self-inductance of the secondary coil.

Plugging the last eq. into the first, we obtain a differential equation for $I_2$. Since there is a term containing $I_1$, the current in the secondary will definitely be influenced by the primary current.

5. May 20, 2012

### nemesiswes

I figured the primary should still induce a voltage. Granted I did not do the math to figure it out, I figured there should be. Math is great and all but for me, to really understand something, I have to be able to visualize what is happening. Only then can I really understand what the math is saying. I still don't know calculus though, lol but i am learning little by little.

As for why I thought there should still be a voltage induced is because since the primary's magnetic flux has a rate of change and it is the rate of change that induces the voltage, it should not matter how much bigger the secondary's magnetic flux is. That rate of change is like the vibrations in the bubble, they can move through the primary's flux and through the secondary's flux even if the secondary is much bigger. The reason the primary eventually after a finite time pulls more current is because the decrease in it's own magnetic flux (since the secondary is over powering it , both fluxes are in the same direction, opposing each other, the 200W battery) which because the magnetic flux around the primary is less, that means less back-emf on the primary and thus a higher net voltage to drive more current. Then when the primary pulls more current it reestablishes the flux to it's original value and this is how the power transfer works.

I think, lol.

I am probaly wrong and if I am, then could you provide maybe a more visual way of how the voltage is induced and the power transfer actually happens. I am not that great with math yet, so yeah, lol.

Last edited: May 20, 2012
6. May 21, 2012

### Jano L.

Your description is hard to follow, but I think it is correct.

You seem to assume that the emf in secondary is solely due to changing flux of B due to primary coil, However, this is not accurate, because there is also some emf induced in secondary due to changing flux of B of the secondary itself (this is described by the self - inductance L).

I can recommend you hyperphysics site:

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

and standard textbooks on electricity like Feynman's lectures on electricity. Learn calculus as soon as you can, it is like a language of physics.