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This is the solution to a problem asking for the charge density ρ given the electric field E, using the equation ∇⋅E = ρ/ɛ.
Why is it a legal move to multiple before and after the operator? It changes the answer (of course) to something that can be simplified and actually makes sense, but I don't see why this is the correct way to do it.
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Do you guys understand what I'm asking?
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>>8718173
Yeah.. I stared at it for a good 4~6 minutes and at first I wanted to argue linearity but that's such a bullshit reason. I can't tell why. If you don't multiply by it, then it clearly changes the answer, you can see it on the first term easily.
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>>8718159
It's a linear operator?
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>>8718181
Correct me if I'm wrong, but I'm pretty sure the del operator is not linear.
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>>8718184
Del should be linear, prove it by plugging in a homogenous term and looking at uniqueness.
It's for sure linear in cartesian.
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If you where not using this shit DEL / NABLA notation you would see that your formula in red is the gradient while they apply the divergence in the calculus
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>>8718206
The terms of the del operator don't change if I'm doing a scalar multiplication of del versus a dot product involving del, so I don't see what you mean when you say that the formula in red only applies to gradience and not divergence.
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divergence involves a matrix produxt and you can clearly see here that the result is different from the gradient
https://en.wikipedia.org/wiki/Del_in_cylindrical_and_spherical_coordinates
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>>8718159
I don't think I understand what you mean, but the math looks good to me
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>>8718220
oh....
wrong equation
thought they were same for gradience and divergence
thanks, this makes sense now
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