If anyone is interested...
The equation for the ellipse is ## x^2/a^2 + y^2/b^2 = 1##, ##a > b##. Substituting ##a## for ##d## above and solving for ##y##, the equations become
\begin{align*}
& 2\pi Gm\sigma \int_{-a}^{a}[1 - \frac{(a-x)}{\sqrt{(b^2-(b^2/a^2)x^2)+(a-x)^2}}]dx \\
\text{or} \\
&...
Your last paragraph would never influence an electron with enough pressure to support the mass of a star.
Your first paragraph, however, is spot on and intuitive.
And I'm good...thanks for your response.
the answer above was: "restoring force bringing back neutrality"
Does this mean,
bring back (to neutrality) = zero electron expansion or prevents electron expansion
or
expand till (neutrality) = electrons expand till force equals fermi pressure = some electron expansion
From Wikipedia : White dwarfs resist gravitational collapse primarily through electron degeneracy pressure
What prevents electrons from expanding radially through the space between the ions (carbon, say)?
Suppose you have a sphere of radius a of positive charge, and a concentric shell from a to b of negative charge. The positive charge is equal to the negative charge. (non-conducting, uniform density)
Is there an outward pressure at a of kqq/a2/(4πa2) - with pressure decreasing with radius...
Using Lane Emden and n = 3 (relativistic), I calculate the correct mass -- the Chandrasekhar mass (about 1.4 Msun)
The equation goes Mtotal ∝ a3, because at n=3, the density, ρ, cancels out.
a2 ∝ K/G = Kg2 → a3 ∝ Kg3. Here K ∝ h c or Kg m3/sec2 and G ∝ m3/Kg/sec2
This implies the mass, Mtotal...
What happens to the material not involved in the core collapse of a supernova? This would be the outer portion of a star or any cloud that surrounds the star. All material to infinity or does some material remain close -- gravitationally close that might collapse if it could. thanks
I would like to get a more physical interpretation of conduction electrons (fermi gas) in a metal. I imagine ionized valence electrons close to the ions, with the fermi level (highest energy electrons) of the gas participating in conduction. A point of confusion for me...the first ionization...