# Any difference between induced EMF of an air coil vs with magnet core?

1. Mar 27, 2012

### yungman

$$EMF=-\frac{\partial \Phi}{\partial t}$$

If two identical coil with same turns of wire and same dimension ( same cross section area in the middle), one has only air and the other has a magnet core. If the two placed in an uniform varying magnetic field, is there any difference in the induced EMF?

From my understanding, induced EMF is independent to the core material because the amplitude of the external field B is constant so is the area in the middle is constant.

$$\Phi=|\vec B|S\;\hbox { if }\; \vec B \;\hbox { is parallel to }\;\vec S$$

2. Mar 27, 2012

### K^2

Well, yeah, given same dB/dt, you'll get the same EMF, but adding iron core usually increases the B field inside the coil, and thereby, increasing EMF.

3. Mar 27, 2012

### yungman

I thought the B field is constant regardless the core material. In magnetic circuit, $\Phi$ is constant in a closed loop regardless of material of the core. And Faraday's Law don't include inductance.

Is there any formula that show that's an iron core change the B inside the core?

4. Mar 27, 2012

### K^2

Well, imagine that you have something like Hemholtz Coils producing a B field. Place a feromagnetic inside. You'll end up with more field lines going through the feromagnetic, increasing the field density inside it. If you now place a small coil around that feromagnetic, send AC through your Hemholtz coils, you'll get stronger EMF on your small coil than you would without feromagnetic in the same arrangement.

Basically, placing dia/para/feromagnetic in the magnetic field, distorts the field, and you can use that to increase/decrease the EMF.

5. Mar 27, 2012

### yungman

What is a Hemholtz coil?

I understand about the field generation part where

$$\nabla \times \vec B= \mu_r\mu_0 NI\;\hbox { where N is number of turns, I is current through the wire.}$$

This said if $\mu_r\;$ is higher, more B produced by by the coil with a given current.

But my question is on the receiver side only. GIVEN the B is constant produced from a source from some distance away and is uniform. I don't see anything support the assertion that the induced EMF will be different from the receiver coil whether there is magnetic material or air core. I don't see it as the case like in the transformer where the core make a difference.

6. Mar 27, 2012

### K^2

That's the thing. Placing feromagnetic in uniform field distorts the field, and you no longer have a uniform field. That's a classic E&M problem. Take a sphere with μ=/=μ0 into an external uniform field, and compute the resulting field. Try it out.

7. Mar 27, 2012

### yungman

That's what I gathered. But what is the amount of change? Assume the field is a uniform field.

My thinking is the magnet in the receiving coil deflect the external field. But in a uniform field, say because of the magnet deflection, instead of the part of the field that supposed to pass through the coil, it got deflected. Instead, the field from next door got deflected into and through the coil. But in a uniform field, the magnitude is the same, so the induced EMF should be the same.

Or are you saying because of the iron core, it actually suck more field from the surrounding through the coil? This means whether the core is a magnet or not has no bearing, it is the $\mu_r\;$ that makes the difference.

8. Mar 27, 2012

### yungman

The reason I ask is because I am experimenting with noise cancellation using a second coil. I have two coil in series, one has magnet core. It pickup noise from the surrounding. Then I put another coil with identical bobbin and exactly the same amount of wire turns and construction and in opposite direction winding as the coil with magnet core. My finding is there are no obvious difference in the ability of the second coil to cancel the noise whether it has air core or magnet core.

With that, I believe the difference cannot be over 10% as I am looking a the difference signal, it is much more noticeable if there is a change in one coil.

9. Mar 27, 2012

### K^2

That's basically what happens. The question, though, is what the field geometry is to begin with. Maybe you can make a sketch of your setup?

10. Mar 27, 2012

### yungman

The field is from say a florescent light from quite a few feet away. The two coils are side by side facing in the same direction.

Basically you answer my question that with the ferromagnetic material as the core, you bend the field to get my field lines through the coil so you get more EMF. The question is how much more. From my experiment, I think the difference is less than 10%.

11. Mar 27, 2012

### K^2

I think it's going to vary a lot with field geometry, core geometry, and core material. I wouldn't be at all surprised if in your case the difference was small.

12. Mar 27, 2012

Thanks

Alan