# I Permeability in free space

1. Nov 30, 2016

### MarSuper

In free space does permeability increase or decrease when a magnetic field is applied?

2. Nov 30, 2016

### Staff: Mentor

3. Nov 30, 2016

### MarSuper

I noticed while reading else where on the internet that certain materials have a relative permeability for the material. I was wondering since permeability increases in ferromagnetic materials when an external magnetic field is applied I was wondering if that was also true for free space.

4. Nov 30, 2016

### tech99

Ferromagnetic materials have a non linear characteristic, so the slope changes with applied field, but free space is linear, so the permeability does not change.

5. Dec 1, 2016

### MarSuper

Just to be sure. It seems to me that the permeability although it is a constant in free space would change when a magnetic field is applied. As an example the speed of light is a constant in free space until it encounters a gravitational field. Light slows down when it encounters a gravitational field. So I am wondering does a magnetic field in a vacuum change the permeability from its normal value. If so does it increase or decrease. I was wondering if anyone tried to measure permeability in space when a magnetic field is applied to it.

6. Dec 1, 2016

### Staff: Mentor

It does no such thing. Gravitational time dilation will redshift light that is climbing up out of a gravity well and blueshift light that is falling into one, and gravitational lensing will change the direction that light is moving, but light always moves at $c$ in a vacuum. (If you think you've heard something else, chances are that you or your source are either misunderstanding or misrepresenting a coordinate velocity).

7. Dec 2, 2016

### Meir Achuz

muzero Is not really a physical constant. In fact, muzero/4pi=10^-7 because of the change from CGS units to MKS units, with another factor of 10^-2
because the current unit of 1 A was chosen to equal 0.1 absolute amperes. The only way muzero could change is if the number 10 changed or pi changed.

8. Dec 5, 2016

### MarSuper

Nugatory think we may have a bit of misunderstanding.

They call it relativity for a reason. The speed you measure light traveling depends on your reference frame when a gravitational field is present. If you are in the rest frame of the mass that is generating the gravitational field, then the speed of light can be calculated from the Schwarzschild metric. This link presents a nice derivation: http://mathpages.com/rr/s6-01/6-01.htm

In general, the speed of light depends on the gravitational field as well as the where and what direction the beam of light is. The speed of light is not a simple scalar in a gravitational field, but rather a tensor! So if I am looking at the speed of light outside of the gravitational field it can appear as being slowed down. So you are right as long as I am measuring the speed of light from within the frame of reference of the gravitational field.

9. Dec 6, 2016

### MarSuper

@Meir Achuz If what you say is true then permeability should change in the presence of a gravitational field. According to Einstein the value of Pi changes in space because the bending of space makes space non-Euclidean.

10. Dec 6, 2016

### Meir Achuz

Pi is a mathematical number that can be defined by a definite integral or a power series. This number cannot be affected by a gravitational field.
If Einstein said anything, it was not that this number changed,

11. Dec 7, 2016

### MarSuper

you can interpret this as you will.

Einstein followed the line of reasoning that began with the "happiest thought" of his life. While still at the Swiss patent office, he conducted one of the famous thought-experiments. Einstein imagined a circle spinning in space. The center of the circle did not move, but its circumference was moving quickly in a circular direction. Einstein compared what happens in several reference frames, a standard tool he had used in developing the special theory of relativity. He concluded, using his special relativity, that the boundary of the disk contracted as it spun. There was a force acting on the circle at the boundary - the centrifugal force - and its action was analogous to that of a gravitational force. But the same contraction that affected the outer circle left the diameter unchanged. Thus, Einstein concluded, in a way that surprised even him, the ratio of the circle to the diameter was no longer pi. He deduced that in the presence of a gravitational force (or field), the geometry of space is non-Euclidean.

There you go, that is what Einstein's thoughts were on the subject.

Last edited: Dec 7, 2016
12. Dec 18, 2016

### Meir Achuz

Yes, Einstein wrote "the ratio of the circle to the diameter was no longer pi.".
That says that the ratio of the circumference to the diameter changed, but the number pi did not.

13. Dec 24, 2016

### electro-physics

With out going in deep details permeability is basically flux density per magnetizing force. When we wind some piece of wire around a ferrite core and apply high frequency switching on it it generates magnetic flux. This flux increases with increase in applied conditions like volt-second. The ease of passing flux is represented by permeability and more correctly relative permeability as we are considering core material to air or vacuum. When whole piece of core has maximum limit of flux passage then it starts passing through air i.e. outside the core. But we know that an air coil has very small impedance so the transistor that was switching this coil on ferrite core may very soon come to destruction. When flux starts passing through air the previous almost linear relation of flux density to magnetizing force which represents its permeability does not held same as core gets saturated.

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