# Induced emf and flux in a transformer, conceptual question

1. Jan 16, 2013

### Kale

Hey Folks, I am a third year electrical engineering student and just want to clarify a concept involving electromagnetics/transformers.

When supplying magnetization current to a transformer (assume sinusoidal), this induces a time changing magnetic flux in the core. The time changing magnetic flux then induces an emf.

1) Is this emf a result of an induced electric field in the core of the transformer, or in the coil?
-Since the core and coil are both conductors, would it be both? I understand eddy currents trying to oppose the change in flux, so we may ignore that.

2) Would this emf (therefore electric field) induce another magnetic field, then the magnetic field induces an electric field on and on and on?
-Since we can infinitely differentiate a sinusoid, there should be an infinite succession of mutual induction.

3) If 2) is the case, how do we take that into consideration when analyzing a transformer?

∇×E = -dB/dt and e(ind) = -Nd$\phi$/dt

Thank you!

2. Jan 16, 2013

### Kale

I originally posted this in the electrical engineering section, thought it would be appropriate here as well.

Hey Folks, I am a third year electrical engineering student and just want to clarify a concept involving electromagnetics/transformers.

When supplying magnetization current to a transformer (assume sinusoidal), this induces a time changing magnetic flux in the core. The time changing magnetic flux then induces an emf.

1) Is this emf a result of an induced electric field in the core of the transformer, or in the coil?
-Since the core and coil are both conductors, would it be both? I understand eddy currents trying to oppose the change in flux, so we may ignore that.

2) Would this emf (therefore electric field) induce another magnetic field, then the magnetic field induces an electric field on and on and on?
-Since we can infinitely differentiate a sinusoid, there should be an infinite succession of mutual induction.

3) If 2) is the case, how do we take that into consideration when analyzing a transformer?

∇×E = -dB/dt and e(ind) = -Ndϕ/dt

Thank you!

3. Jan 16, 2013

### VantagePoint72

The back emf is due to the induced electric field in the coil. You will also get an electric field in the core of the transformer, but this is not part of the circuit containing the power source (the coils are electrically insulated from the core).

Yes. The "on and on and on" is electromagnetic radiation, which caries away some energy from the transformer at the frequency of the current.

You can treat the transformer as an oscillating magnetic dipole. There is a standard formula for the power radiated by a changing magnetic dipole (5.7.18 here), though it's most easily derived in the relativistically covariant formulation of Maxwell's equations. Obviously, this power needs to be provided by the power source to your circuit and hence solving for voltage in $P=IV$ will tell you the total back emf corresponding to radiation that your transformer has to overcome. Magnetic dipole radiation goes as the fourth power of frequency (as you can see from that formula if you substitute in a sinusoidal magnetic moment) and so will be extremely small at the standard (in North America) current frequency of 60Hz.

Last edited: Jan 16, 2013
4. Jan 16, 2013

### Studiot

Why do you think the induced EMF is a result of an electric field, not a magnetic one?

You do understand Lenz' Law?

5. Jan 16, 2013

### Kale

I do understand Lenz' Law, sorry I should have made myself more clear. An induced emf arises to reduce the change in magnetic flux in a by conductor, in this case the conductors would be the coil and the core.

The fact that there is an induced emf indicates that there is an electric field, the emf used in transformer analysis applies to the coil.

Because the core is also conducting, the changing flux will also induce emf in the core, but this is negligible in transformer analysis?

6. Jan 16, 2013

### VantagePoint72

I answered this above: the core is not connected to the powered circuit so the induced electric field in it doesn't contribute to the back emf.

Edit: Ah, it looks like your two threads were merged, maybe that's why you didn't see my first reply.