# Calculating Core & Currents for Coils and Cores

• Engineering
• Chris Fuccillo
In summary, the conversation discusses calculating the core and currents required for a coil and core, as well as the confusion surrounding the external magnetic field. The problem involves a 5 turn coil on a ferromagnetic core that is placed in a uniform external magnetic field. The current is then turned on in the opposite direction to the external field to saturate the core in the direction of the coil's magnetic field. The relevant equations include H = Ni/(2πr) and B = u * H. The solution may involve numerical simulation or driving the coil with a DC voltage bias and AC voltage signal to detect the onset of saturation. The shape of the core is not specified, but assuming a straight core may make the solution more straightforward.
Chris Fuccillo
Homework Statement
A 5 turn coil is wound on a ferromagnetic core. The wound core is then placed in a external uniform magnetic field. The current is then turned on to flow through coil in the direction to generate a magnetic field 180 degrees opposite the external field. How much current and how large of and H field will be will be required to cause the core to saturate in the direction of the coils magnetic field/ opposite the external fields direction

Core information:
Turns on core N = 5
Saturation 1.56 T
µᵣ = 600,000
"µ = µₒ x µr" µ = 7.5398
Magnetic path r = 0.00115m

External magnetic field:
B(ext) = 0.35 T

vacuum µₒ = 4π x 10-7 =

Find the current i H field required to saturate the core H = , i =
Relevant Equations
H = Ni/(2πr)
B = u * H
I can easily calculate the core and currents required for the coil and core, i get confused do the the external field, any help please.

Rasel Osman
Chris Fuccillo said:
Homework Statement:: A 5 turn coil is wound on a ferromagnetic core. The wound core is then placed in a external uniform magnetic field. The current is then turned on to flow through coil in the direction to generate a magnetic field 180 degrees opposite the external field. How much current and how large of and H field will be will be required to cause the core to saturate in the direction of the coils magnetic field/ opposite the external fields direction

Core information:
Turns on core N = 5
Saturation 1.56 T
µᵣ = 600,000
"µ = µₒ x µr" µ = 7.5398
Magnetic path r = 0.00115m

External magnetic field:
B(ext) = 0.35 T

vacuum µₒ = 4π x 10-7 =

Find the current i H field required to saturate the core H = , i =
Relevant Equations:: H = Ni/(2πr)
B = u * H

I can easily calculate the core and currents required for the coil and core, i get confused do the the external field, any help please.
Yeah, the presence of the external "uniform" magnetic bias field can be quite complicated to deal with, but maybe they are saying to assume that the bias field that goes through the core still has the value of the external bias field of ##B_{ext} = 0.35T##. That will not be true in real life because the presence of the high-##\mu## material will concentrate the external field into the core. But figuring out how much that concentration is requires numerical simulation usually.

So if you assume that the bias field in the core from the external field is 0.35T one direction, and the saturation field is 1.56T (the other direction), what coil current does it take to generate a field that counteracts the bias field and takes the core to saturation?

Here is a figure showing the situation in real life, with magnetic field concentration due to high-##\mu## material (I could only find this image for a magnetic shield, but you get the idea...):

https://qph.fs.quoracdn.net/main-qimg-5c58b3c4b703301c80059e5005c4a215.webp

berkeman said:
Yeah, the presence of the external "uniform" magnetic bias field can be quite complicated to deal with, but maybe they are saying to assume that the bias field that goes through the core still has the value of the external bias field of ##B_{ext} = 0.35T##. That will not be true in real life because the presence of the high-##\mu## material will concentrate the external field into the core. But figuring out how much that concentration is requires numerical simulation usually.

So if you assume that the bias field in the core from the external field is 0.35T one direction, and the saturation field is 1.56T (the other direction), what coil current does it take to generate a field that counteracts the bias field and takes the core to saturation?

Here is a figure showing the situation in real life, with magnetic field concentration due to high-##\mu## material (I could only find this image for a magnetic shield, but you get the idea...):

https://qph.fs.quoracdn.net/main-qimg-5c58b3c4b703301c80059e5005c4a215.webp

View attachment 267017
your correct this is a "real life" question this will be a coming experiment .

In a sense how do I calculate the extra current to overpower the persistent magnetic bias field. I guess my question boils down to when calculating the current required for the H(A/m) field to cause B = u * H to be 1.56 T. To over come the bias is it the difference between negative bias and the positive saturation?
Bias = -0.35 T
Core +1.56 T
Difference = 1.91 T
so I would need to drive an H field to generate 1.91 T swing in the core using its µ value even though the core could not get that high and it directional thing or to overcome the bias field do I have to calculate enough current using B = µₒ * H "ie" free space until B goes from -0.35 T to 0 T, then use B = u * H "core" till it hits saturation.

I guess I need to know if I use the cores u or or Vacuum µₒ when overcoming a external persistent bias field the coil is in? or if I am missing something else lol.

Also thank you for the help

I'm glad to help. If this is for a real-world experiment, IMO it would be easiest to drive the coil with a DC Voltage bias plus an AC Voltage signal and watch the coil current waveform to see the onset of saturation. Do you know how to probe the AC current versus input voltage waveform to detect the onset of saturation?

Otherwise, you will need to buy a license to COMSOL and learn how to use it, IMO. Fun to do if you have lots of time to learn it, but not so fun if you need results quickly without time for the learning curve...

I don't see where the shape of the core is specified in the OP.

Considering the phrasing and context (magnetic field 180 degrees opposite the external field.), I used the KISS approach and assumed a straight core was to be used.

Seems like that would make the solution rather straightforward.

Cheers,
Tom

berkeman
Tom.G said:
I don't see where the shape of the core is specified in the OP.

Considering the phrasing and context (magnetic field 180 degrees opposite the external field.), I used the KISS approach and assumed a straight core was to be used.

Seems like that would make the solution rather straightforward.

Cheers,
Tom
Ok pls what is the solution

Chris Fuccillo said:
Ok pls what is the solution
It's your schoolwork problem, so you need to show us your work first...

Tom.G

## 1. How do you calculate the core and currents for coils and cores?

To calculate the core and currents for coils and cores, you will need to know the number of turns in the coil, the cross-sectional area of the core, the permeability of the core material, and the applied voltage or current. You can use formulas such as Ampere's Law and Faraday's Law to calculate the magnetic field strength and current in the coil. Alternatively, you can use simulation software or experimental methods to determine these values.

## 2. What is the purpose of calculating core and currents for coils and cores?

The purpose of calculating core and currents for coils and cores is to understand and optimize the performance of electromagnetic devices such as transformers, motors, and generators. By accurately calculating the magnetic field strength and current in the coil, we can determine the efficiency, power output, and other important characteristics of these devices.

## 3. How does the core material affect the calculation of core and currents?

The core material plays a crucial role in the calculation of core and currents for coils and cores. The permeability of the core material determines how easily the magnetic field can pass through it, which affects the strength of the magnetic field and the amount of current needed to produce it. Different core materials have different permeabilities, so it is important to choose the right material for the desired performance of the device.

## 4. Can the calculation of core and currents be affected by external factors?

Yes, the calculation of core and currents for coils and cores can be affected by external factors such as temperature, humidity, and external magnetic fields. These factors can alter the properties of the core material, which can in turn affect the magnetic field strength and current in the coil. It is important to account for these factors in the calculation to ensure accurate results.

## 5. Are there any limitations to the calculation of core and currents for coils and cores?

Yes, there are some limitations to the calculation of core and currents for coils and cores. These calculations assume ideal conditions, such as a uniform magnetic field and a perfect core material. In reality, there may be variations in the magnetic field and imperfections in the core material, which can affect the accuracy of the calculation. Additionally, complex geometries and non-linear materials may require more advanced mathematical models for accurate calculations.

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