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In the derivation of the electric field inside a non conducting sphere, We still use the permittivity of free space even though we are in a medium.

The same applies for ampere's law in a solid wire.

http://physics.bu.edu/~duffy/semester2/c15_inside.html

https://stuff.mit.edu/afs/athena/course/8/8.02-esg/Spring03/www/8.02ch24we.pdf

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    $\begingroup$ It's a fundamental law, it's always true whether you're in a medium or not. $\endgroup$
    – knzhou
    Commented Mar 24, 2018 at 10:17

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You will note in this table that the relative permeability of non-ferromagnetic materials is very close to one.
For example:
Air 1.00000037 Copper 0.999994

Then as this table shows for a lot of gases the relative permittivity is also close to one eg air 1.000536, argon 1.000513. However if the material can be polarised then one would have to multiply the permittivity of free space by the relative permittivity eg Sulphur 3.5, Marble 8

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  • $\begingroup$ So for non conducting material, the assumption is based on that Er = 1? $\endgroup$ Commented Mar 24, 2018 at 11:14
  • $\begingroup$ @user3733086 A good example is the parallel plate capacitor. If there is air between the plates then $\epsilon_0$ is used but if there is sulphur between the plates then one needs to use $\epsilon_{\rm sulphur}$. $\endgroup$
    – Farcher
    Commented Mar 24, 2018 at 11:32
  • $\begingroup$ It is true that we are living in a medium, but using permittivity of free space as a reference point helps to write up formula; instead of writing many equations, we can write one equation with an empirical coefficient: dielectric constant. $\endgroup$
    – user115350
    Commented Mar 24, 2018 at 17:48

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