How to find inductance of a coil with two concentric ferromagnetic cores?

jam1234
Messages
3
Reaction score
0

Homework Statement



This isn't exactly a homework question so there aren't any data/numbers to work with. I just want to know what to do if there are two ferromagnetic cores inside a coil of wire, arranged as concentric cylinders. Or how to account for the air gap between the core and the coil?

Homework Equations



L = μN2A/l

The Attempt at a Solution



Should it be treat as a series circuit? Or maybe parallel? Or do you weight the contributions of the relative permeabilities by the fraction of the area inside the coil they occupy?
 
Physics news on Phys.org
jam1234 said:

Homework Statement



This isn't exactly a homework question so there aren't any data/numbers to work with. I just want to know what to do if there are two ferromagnetic cores inside a coil of wire, arranged as concentric cylinders. Or how to account for the air gap between the core and the coil?

Homework Equations



L = μN2A/l

The Attempt at a Solution



Should it be treat as a series circuit? Or maybe parallel? Or do you weight the contributions of the relative permeabilities by the fraction of the area inside the coil they occupy?

Depending on the arrangement, I would guess that the outer core would dominate the inductance -- that is, very little of the B-field would be coupled to the inner core. The outer core would act as a shield for the inner core, IMO.

Do you have an application in mind?
 
berkeman said:
Depending on the arrangement, I would guess that the outer core would dominate the inductance -- that is, very little of the B-field would be coupled to the inner core. The outer core would act as a shield for the inner core, IMO.

Do you have an application in mind?

Well for example to account for the ring of air around a metal core in a solenoid. In some cases this may not be negligible.
 
jam1234 said:
Well for example to account for the ring of air around a metal core in a solenoid. In some cases this may not be negligible.

That's a different situation than the question in your original post (OP). If you have an air gap between the windings and a single core, then that increases the leakage inductance Lk and reduces your magnetizing inductance Lm.
 
berkeman said:
That's a different situation than the question in your original post (OP). If you have an air gap between the windings and a single core, then that increases the leakage inductance Lk and reduces your magnetizing inductance Lm.

I did put the air gap bit in my original question as well. How would you find the inductance of a coil with a metal core and an air gap around it? I don't want to assume it is negligible because it isn't always. Do you just use the relative permeabilities weighted by the areas occupied by the core and air gap?
 
##|\Psi|^2=\frac{1}{\sqrt{\pi b^2}}\exp(\frac{-(x-x_0)^2}{b^2}).## ##\braket{x}=\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dx\,x\exp(-\frac{(x-x_0)^2}{b^2}).## ##y=x-x_0 \quad x=y+x_0 \quad dy=dx.## The boundaries remain infinite, I believe. ##\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dy(y+x_0)\exp(\frac{-y^2}{b^2}).## ##\frac{2}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,y\exp(\frac{-y^2}{b^2})+\frac{2x_0}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,\exp(-\frac{y^2}{b^2}).## I then resolved the two...
Hello everyone, I’m considering a point charge q that oscillates harmonically about the origin along the z-axis, e.g. $$z_{q}(t)= A\sin(wt)$$ In a strongly simplified / quasi-instantaneous approximation I ignore retardation and take the electric field at the position ##r=(x,y,z)## simply to be the “Coulomb field at the charge’s instantaneous position”: $$E(r,t)=\frac{q}{4\pi\varepsilon_{0}}\frac{r-r_{q}(t)}{||r-r_{q}(t)||^{3}}$$ with $$r_{q}(t)=(0,0,z_{q}(t))$$ (I’m aware this isn’t...
Hi, I had an exam and I completely messed up a problem. Especially one part which was necessary for the rest of the problem. Basically, I have a wormhole metric: $$(ds)^2 = -(dt)^2 + (dr)^2 + (r^2 + b^2)( (d\theta)^2 + sin^2 \theta (d\phi)^2 )$$ Where ##b=1## with an orbit only in the equatorial plane. We also know from the question that the orbit must satisfy this relationship: $$\varepsilon = \frac{1}{2} (\frac{dr}{d\tau})^2 + V_{eff}(r)$$ Ultimately, I was tasked to find the initial...
Back
Top