# Magnetic Flux Through a Tilted Medium

• magnetpedro
In summary, the inductance of a ferromagnetic medium shaped as a cylinder with a magnetic relative permeability of μr, tilted with an angle a, is independent of the angle a.
magnetpedro
Imagine a ferromagnetic medium shaped as a cylinder (a ferromagnetic fiber) with a magnetic relative permeability of μr, tilted with an angle a, as shown in the picture.

I would like to prove analytically that the sum of the inductances measured along the x-axis (angle is a) and y-axis (angle is π/2 - a) is independent of the angle a. (Lsum = Lx + Ly independent of a).

Each case, Lx and Ly is also the sum of the inductance of the projections of the fiber in the x and y axis.
My approach consists in using Hopkinson's Law and first determining the Reluctance for each case, and then calculating the Inductance using L= N2/Reluctance, where N is a constant number of turns of a supposed magnetomotive force.

Do you think it's possible?

Thank you very much.

Don't understand your post. What is the inductance of a cylinder?

magnetpedro
marcusl said:
Don't understand your post. What is the inductance of a cylinder?

It's the Inductance of a ferromagnetic medium shaped as a cylinder, that is crossed by a flux produced by a magnetomotive force.

Inductance is a quantity that relates energy stored in a magnetic field to the currents producung the field. It also relates an induced emf to a changing current. You have no currents, hence no inductance.

magnetpedro
marcusl said:
Inductance is a quantity that relates energy stored in a magnetic field to the currents producung the field. It also relates an induced emf to a changing current. You have no currents, hence no inductance.

My mistake, forgot to mention that the magnetomotive force is produced by a current I (constant). That's my current.

Your problem doesn't make sense as stated and suggests that you don't understand inductance. Have you had an undergrad E&M course?

marcusl said:
Your problem doesn't make sense as stated and suggests that you don't understand inductance. Have you had an undergrad E&M course?

Yes I have. I'll try to explain this model.
Imagine that a magnetomotive force is produced by a number of turns N and a current I, being Fmm=N*I.
That magnetomotive force creates a magnetic flux ∅ that only crosses the ferromagnetic cylinder.
The inductance of the ferromagnetic medium/fiber can be determined using the following expressions:

L = N× ∅ / I

∅ = Fmm/R

L = N2/R

where R is the reluctance of the ferromagnetic medium, given by:

R= l/(μ0r*A)

where l is the length of the path of the magnetic flux, μ0 is the magnetic constant (vacuum's permeability), μr is the relative magnetic permeabilty of the ferromagnetic cylinder and A is the area that is crossed by the flux.

These formulas are usually written in terms of the number of turns per unit length n, in which case $L=\frac{n^2l}{R}$. Furthermore, this applies to long solenoids. Since your core is short, this will be an approximation at best.

To your original question, however, inductance is a scalar quantity so you can't break it into x and y components.

marcusl said:
These formulas are usually written in terms of the number of turns per unit length n, in which case $L=\frac{n^2l}{R}$. Furthermore, this applies to long solenoids. Since your core is short, this will be an approximation at best.

To your original question, however, inductance is a scalar quantity so you can't break it into x and y components.

Yes, inductance is a scalar quantity but I can make a projection of the ferromagnetic fiber along x and y, with a length and cross area also projected, calculate both Inductances Lx and Ly, and then the "final" inductance would be L = sqrt(Lx^2 + Ly^2).

Well yes, you could do that, but I don't see the value since L is already independent of your angle, by definition.

davenn

## 1. What is magnetic flux?

Magnetic flux is a measure of the amount of magnetic field passing through a given area. It is represented by the symbol Φ and is measured in units of webers (Wb).

## 2. How is magnetic flux affected by a tilted medium?

When a magnetic field passes through a tilted medium, the angle of the medium affects the amount of magnetic flux passing through it. The flux is reduced when the medium is tilted at an angle to the magnetic field lines, and is maximum when the medium is parallel to the field lines.

## 3. What is the formula for calculating magnetic flux through a tilted medium?

The formula for calculating magnetic flux through a tilted medium is Φ = BcosθA, where B is the magnetic field strength, θ is the angle between the magnetic field lines and the medium, and A is the area of the medium.

## 4. How does the magnetic flux through a tilted medium affect the strength of the magnetic field?

The magnetic flux through a tilted medium does not affect the strength of the magnetic field itself, but it does affect the amount of field lines passing through the medium. This, in turn, can affect the magnetic force experienced by charged particles moving through the medium.

## 5. Can the magnetic flux through a tilted medium be negative?

Yes, the magnetic flux through a tilted medium can be negative. This occurs when the medium is tilted at an angle greater than 90 degrees to the magnetic field lines, resulting in a negative cosine value in the flux formula. A negative flux indicates that the magnetic field is flowing in the opposite direction of the medium.

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