Calculating Core & Currents for Coils and Cores

[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.

 

[berkeman]

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

 

[Chris Fuccillo]

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

 

[berkeman]

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...

 

[Tom.G]

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

 

[Chris Fuccillo]

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

 

[berkeman]

Ok pls what is the solution

It's your schoolwork problem, so you need to show us your work first...