- #1
davidbenari
- 466
- 18
There are problems in classical electromagnetism where they ask you to find the electrical displacement given some geometry (like a sphere or a cylinder) and the dielectric constant ##\epsilon_r##.
The solution to these problems typically employs symmetry arguments along with Gauss' laws for the D field. However, it got me thinking: Is this only valid in the case when the dielectric is linear?
What justifies symmetry arguments for the D field in general? I have a vague intuition about the validity of this, but these arguments aren't as obvious as the case for the E field.
I wouldn't like to say much more because I want a general argument that explains why exploiting symmetry works for the D field.
You could take as an example the case of an infinite cylindrical capacitor with a dielectric in between. (Maybe its linear, maybe not)
Why should the D field be radial in this case? I agree with you it has to look the same at whichever point separated a distance ##s## from the cylinder since the cylinder is infinite, but how would you counter someone who says that it's not perfectly radial but has some inclination as well?
Thanks!
The solution to these problems typically employs symmetry arguments along with Gauss' laws for the D field. However, it got me thinking: Is this only valid in the case when the dielectric is linear?
What justifies symmetry arguments for the D field in general? I have a vague intuition about the validity of this, but these arguments aren't as obvious as the case for the E field.
I wouldn't like to say much more because I want a general argument that explains why exploiting symmetry works for the D field.
You could take as an example the case of an infinite cylindrical capacitor with a dielectric in between. (Maybe its linear, maybe not)
Why should the D field be radial in this case? I agree with you it has to look the same at whichever point separated a distance ##s## from the cylinder since the cylinder is infinite, but how would you counter someone who says that it's not perfectly radial but has some inclination as well?
Thanks!
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