Flux Density in Mutual Induction Solenoid with Core

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Discussion Overview

The discussion revolves around the calculation of magnetic flux density (B) in a mutual induction solenoid, particularly focusing on the effects of core material and current type (AC vs. DC). Participants explore the applicability of established formulas for solenoids in the context of mutual induction and varying currents.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant states the formula for magnetic flux density in a solenoid as B=μnI, questioning the permeability value for soft iron.
  • Another participant suggests an alternative formula B=μnI/l, introducing the length of the solenoid into the discussion.
  • Concerns are raised about the role of direct current (DC) in mutual induction, emphasizing that mutual induction requires changing flux, which occurs with alternating current (AC).
  • A participant notes that the maximum flux density is expected to occur at the peak of the alternating current.
  • There is a reiteration of the linear relationship between magnetic flux density (B) and current (I), with a request for confirmation on the correctness of the solenoid flux formula.
  • Another participant confirms the formula B=μnI/l is correct under the assumption that the solenoid's length is much greater than its radius, reiterating the linear proportionality of B to I.

Areas of Agreement / Disagreement

Participants express differing views on the formulas applicable to mutual induction and the role of current type, indicating that the discussion remains unresolved regarding the best approach to calculate magnetic flux density in this context.

Contextual Notes

Some assumptions about the core material's permeability and the conditions under which the formulas apply are not fully explored, and the impact of solenoid dimensions on the magnetic field distribution is acknowledged but not resolved.

entity314
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For a standard solenoid, I've found that
B=μnI
where
μ = permeability of the core (4π×10^-7 for free space)
n = number of coils
I = current

Firstly, is the permeability of soft iron 0.08, as I found?

Primarily, however, I'm wanting to know if this still applies for a mutual induction apparatus like in
https://www.scientrific.com.au/PDFs/em2220-001.pdf
 
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I think B=μnI/l where l is the length of the solenoid.
 
Keep in mind that nothing interesting will happen with DC currents. Yes, a magnetic field will be generated but you will not get any mutual induction unless your flux is changing (i.e. varying current through one of the coils.
 
leright said:
Keep in mind that nothing interesting will happen with DC currents. Yes, a magnetic field will be generated but you will not get any mutual induction unless your flux is changing (i.e. varying current through one of the coils.
It's for an alternating current.
Presumably the maximum flux density will occur at the current peak?
 
Yes, because
f7c6a5d2ff27b8dae2e9aa5657aa5909a8bc6d8e (sorry, click on the link, I couldn't copy-paste the formula)
and here B is a linear function of the current (I) as I wrote in my first post.
hth
 
Replusz said:
Yes, because
f7c6a5d2ff27b8dae2e9aa5657aa5909a8bc6d8e (sorry, click on the link, I couldn't copy-paste the formula)
and here B is a linear function of the current (I) as I wrote in my first post.
hth
Thanks, that's what I though :)
Is the formula for the flux a solenoid correct though?
 
You mean this: B=μnI/l ?
 
It is correct assuming the solenoids length is much longer than the radius. B can be considered almost homogeneous inside the solenoid.
But in any case B is linearly proportional to I.
hth
 

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