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

• yungman
In summary, Faraday's Law of Induction states that the induced EMF is independent of the core material as long as the amplitude and area of the external magnetic field remain constant. However, adding a ferromagnetic core can increase the field density inside the coil, thereby increasing the induced EMF. Placing a ferromagnetic material in a uniform magnetic field can distort the field and result in a non-uniform field. The amount of change in induced EMF can vary greatly depending on field and core geometry, but is generally less than 10%.
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.

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

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.

K^2 said:
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.

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?

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.

K^2 said:
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.

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.

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.

K^2 said:
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.

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.

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.

yungman said:
Or are you saying because of the iron core, it actually suck more field from the surrounding through the coil?
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?

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%.

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.

Thanks

Alan

## 1. What is induced EMF?

Induced EMF (Electromotive Force) is the voltage that is generated in a conductor when it is exposed to a changing magnetic field. This phenomenon is governed by Faraday's Law of Induction, which states that the magnitude of induced EMF is directly proportional to the rate of change of the magnetic field.

## 2. What is the difference between an air coil and a coil with a magnet core?

An air coil is simply a coil of wire without any magnetic material inside it. On the other hand, a coil with a magnet core has a magnet or magnetic material placed inside the coil. This magnetic material can be a permanent magnet or an electromagnet.

## 3. How does the presence of a magnet core affect induced EMF in a coil?

The presence of a magnet core inside a coil can significantly increase the induced EMF. This is because the magnetic field produced by the core adds to the changing magnetic field, resulting in a larger rate of change and thus a higher induced EMF.

## 4. What are the advantages of using a coil with a magnet core over an air coil?

A coil with a magnet core has a stronger and more consistent induced EMF compared to an air coil. This makes it more useful for applications such as generators and transformers, where a high and stable induced EMF is required. Additionally, the use of a magnet core can also reduce the size and weight of the coil, making it more compact and efficient.

## 5. Are there any disadvantages of using a coil with a magnet core?

One potential disadvantage of using a coil with a magnet core is the added cost and complexity of incorporating the magnetic material. Additionally, the presence of a magnet core can also introduce hysteresis losses, which can reduce the efficiency of the coil. Careful design and selection of materials can help mitigate these drawbacks.

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