# Why is maximum flux attained in transformer when off load?

Can anyone explain to me why the maximum flux in a transformer is attained when off load?

What happens to the flux when on load? Are the flux from the secondary load current and primary load current just leaking out into space? Or are the magnetic particles somehow being canceled or destroyed? Does anyone have an answer instead of just pointing at conditional math equations that don't explain anything?

Another user claimed the load current flux somehow cancels the primary current flux, but this is inadequate as "canceling" doesn't explain what's happening. Two opposing fluxes should both contribute to a lowered permeability of material. If they don't, then why is this? One would have to conclude that the particles or virtual particles (whatever a magnetic field consists of) are literally being transformed/destroyed/significantly altered or something drastic.

The simplest conclusion is that the vast majority of flux generated while a transformer is loaded should be leaking out into space around the core. But I haven't heard anyone say this. I've certainly never run the experiment myself. Does anyone know if the magnetic field around the outside of a core goes sky high when you put it on load?

• Did you see the final addition i put on my answer for your previous question about transformers? Commented May 31, 2013 at 17:52

Look at the following scenarios and then it should be clearer why maximum transformer flux happens when off-load: -

The above are perfect idealizations of inductors and transformers. And if you are having problems with any of the steps then maybe someone else can do this question some justice.

Why is flux greatest when off-load - if there were no-losses in the windings (R or leakage inductance) then off-load or on-load the flux in the core remains exactly the same (scenario 4). But, because the secondary current causes small volt-drops in the primary winding, the voltage that is able to magnetize the core is slightly reduced thus the flux in the core is slightly reduced and the core is less able to saturate.

The permeability of the material (when not close to saturating) is determined by the physical properties of the material and not the opposing fluxes in primary and secondary due to load current.

The vast majority of flux does not leak into space around the core - it is contained within the core and cancels out to zero for load-currents leaving what was originally there - the magnetizing flux.

When a turns ratio is applied ampere-turns from primary might be 1 x 10 whereas on the secondary (for 10:1 turns ratio) they will be 10 x 1 - ampere-turns drive flux and these cancel out just the same as a 1:1 transformer.

Here is the link to the question posed by Jim related to this one.

Lenz's Law Lenz's law says

"An induced current creates a magnetic field that opposes the changing flux that initially gave rise to the induced current".

Bar magnets This is not the same in bar magnets held N-N and S-S. In Bar magnets (held steady wrt each other) there is no induction and therefore only a force exists and I think this is to do with Newtons 3rd Law?

Twisted pair cable Also think about twisted pair cable - there is no net flux emanating beyond a small distance. of course there are very local fluxes around each wire but these cancel at a very short distance.

• Well that's cool. But I guess I need a person more knowledgeable on the physics to explain why the magnetic fields simply "cancel". If you place two permanent magnets with both North sides toward each other, the fields don't really cancel as far as I know. They repel each other's flux lines and the field distorts. Evidentally, the behavior of flux induced from the electromagnet on the core is different, and not well understood. Commented Jun 2, 2013 at 14:24
• @Jim - your bar-magnet analogy is good and I shall endevour to answer it once I've got me brain in gear!! Commented Jun 2, 2013 at 15:04
• @Jim - Lenz's law is the answer although you might not accept this explanation. Any induced current creates a magnetic field that opposes the changing flux that initially gave rise to the induced current. In Bar magnets (held steady wrt each other) there is no induction and therefore a force exists and I think this is to do with Newtons 3rd Law. Also think about twisted pair cable - there is no net flux emanating beyond a small distance. of course there are very local fluxes around each wire but these cancel at a very short distance. Commented Jun 3, 2013 at 15:18
• Andy, bar magnets in motion behave the same way in terms of their repelling nature -- i.e. Putting them in motion doesn't cause their fields to cancel one another. Secondly, Lenz's Law only states that an opposing field is created. It doesn't state why that field would cancel out the initial flux instead of simply repelling it. Commented Jun 3, 2013 at 23:12

The flux in a transformer is maximum at no load because only a small amount of current is drawn by the primary at the no-load condition. As the load (secondary) current increases, the primary tries to draw a proportional amount of current to counter the demagnetizing effect of secondary current. However, the primary current doesn't really exactly cancel out the effect of secondary and hence the resultant flux is a slightly lower value.

Why can primary not cancel the effect of secondary totally? It is because if the primary current has to increase, it has to be at the expense of induced emf (E) since they are related as I=(V-E)/Z. (Note that V, the voltage applied at primary is constant). Hence E and correspondingly the flux settle for a new (lower) value such that more current can be drawn and a stable equilibrium is achieved.