Does isotropy depend on the location of the origin from where we see the medium?

Asked Aug 29 '19 at 13:18

Active Aug 29 '19 at 16:00

Viewed 60 times

Let us say we have a charged non-conducting sphere having a spherically symmetrical charge density $\rho (r)$ that decreases as $r$.

Ignoring all other properties, If we positon ourselves in the center of the sphere, the medium will appear isotropic because of the spherical symmetry charge distribution. But if we were to change our position to somewhere else other than the origin, the medium would no longer appear isotropic.

So does the isotropy of a medium depend on where we view it from? And if we say a given material is isotropic, should we understand this as it being isotropic with reference to some "special" point?

edited Aug 29 '19 at 16:00

asked Aug 29 '19 at 13:18

Hilbert

1,242

1

While what you describe is spherically symmetric, I would not call it isotropic. If a special origin is needed, your material is not isotropic. – Jon Custer Aug 29 '19 at 14:15
@Jon Custer So in definitive, a material is isotropic when its properties are independent of the direction for every point in the material chosen as our reference for direction? – Hilbert Aug 29 '19 at 14:22
Yup, that summarizes it... – Jon Custer Aug 29 '19 at 15:11
@Jon Custer Just to be sure, doesn't this definition imply every isotropic medium is homogeneous? – Hilbert Aug 29 '19 at 15:35
3

Possible duplicate of What is difference between homogeneous and isotropic material? – Anyon Aug 29 '19 at 16:07

Does isotropy depend on the location of the origin from where we see the medium?

0 Answers0