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So, I was trying to find a rigorous mathematical derivation of gauss's law(please I don't want to hear again any field lines nonsense) and I stumbled upon jackson's proof which uses the solid angle concept and seems a solid enough proof(stupid joke
).The problem is that it's the first time I come in contact with solid angles and I don't get a certain part
Eda=(q/4πε)(1/r^2)cosθda=(q/4πε)dΩWhy
(1/r^2)cosθda=dΩ? (intuitively it makes sense but what is the actual proof)
I'd appreciate if someone gave a clear from zero definition of solid angle
Say we've proven Φ=Qen/ε
if the charge lies outside of the surface how do you prove that the total flux is zero?
Is there a solid angle approach or stoke's theorem is the easiest way?
Forgive me for not using latex it's my first post
).The problem is that it's the first time I come in contact with solid angles and I don't get a certain partEda=(q/4πε)(1/r^2)cosθda=(q/4πε)dΩWhy
(1/r^2)cosθda=dΩ? (intuitively it makes sense but what is the actual proof)
I'd appreciate if someone gave a clear from zero definition of solid angle
Say we've proven Φ=Qen/ε
if the charge lies outside of the surface how do you prove that the total flux is zero?
Is there a solid angle approach or stoke's theorem is the easiest way?
Forgive me for not using latex it's my first post
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