# Induced emf and flux in a transformer, conceptual question

• Kale
In summary, a transformer induces an emf that is due to the changing magnetic flux in the core. This emf is small due to the low frequency of the current being supplied to the transformer.
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!

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!

Kale said:
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.

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).

Kale said:
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.

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

Kale said:
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

You can treat the transformer as an oscillating magnetic dipole. There is a standard formula for the power radiated by a changing magnetic dipole (http://www.scribd.com/doc/56933596/66/Radiated-power-magnetic-dipole-radiation 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:
Is this emf a result of an induced electric field in the core of the transformer, or in the coil?

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

You do understand Lenz' Law?

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?

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

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.

## What is induced EMF in a transformer?

Induced EMF, or electromotive force, is the voltage that is created in a transformer due to the changing magnetic field. It is responsible for the transfer of electrical energy between the primary and secondary coils of the transformer.

## How is induced EMF related to flux in a transformer?

Induced EMF is directly proportional to the rate of change of flux in a transformer. This means that as the flux increases or decreases, the induced EMF will also increase or decrease.

## What factors affect the induced EMF in a transformer?

The amount of induced EMF in a transformer is affected by the number of turns in the primary and secondary coils, the frequency of the alternating current, and the magnetic permeability of the core material.

## Can induced EMF be negative in a transformer?

Yes, induced EMF can be negative in a transformer. This can occur when the rate of change of flux is decreasing, causing the induced EMF to have an opposite direction compared to the applied voltage.

## How does the transformer's design affect the induced EMF?

The design of a transformer, such as the number of turns in the coils and the material of the core, can affect the amount of induced EMF. A transformer with more turns and a higher magnetic permeability in the core will have a higher induced EMF.

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