Satisfying visual for Gauss's law I was studying Gauss law…
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Satisfying visual for Gauss's law
I was studying Gauss law today, which states that the electric flux through an enclosed surface is simply the charge enclosed divided by the permittivity of free space.
I understood the derivation for a closed sphere with a charge located at the center, which was fairly simple. But I could not quite intuitively grasp why the formula Q/(e0) was the same for any shape surface, with the charge located anywhere inside. Then it clicked.
https://imgur.com/a/MTBAYem
Here is a visual of my intuition. The first sphere represents the simple case with a uniform sphere and a center charge. The second diagram is the bridge to the more complex case. The key is that the total flux does not depend on the distance of the sphere surface to the charge. Therefore the flux through two different size spheres are the same.
The third and fourth diagrams stretch this concept to nonuniform surfaces and a charge located offcenter. This visualization helped me a lot.
You can divide up the surfaces a lot more than my 16 times, meaning you can create any arbitrary surface at any location relative to the charge and the flux will be the same.
#science
source
I was studying Gauss law today, which states that the electric flux through an enclosed surface is simply the charge enclosed divided by the permittivity of free space.
I understood the derivation for a closed sphere with a charge located at the center, which was fairly simple. But I could not quite intuitively grasp why the formula Q/(e0) was the same for any shape surface, with the charge located anywhere inside. Then it clicked.
https://imgur.com/a/MTBAYem
Here is a visual of my intuition. The first sphere represents the simple case with a uniform sphere and a center charge. The second diagram is the bridge to the more complex case. The key is that the total flux does not depend on the distance of the sphere surface to the charge. Therefore the flux through two different size spheres are the same.
The third and fourth diagrams stretch this concept to nonuniform surfaces and a charge located offcenter. This visualization helped me a lot.
You can divide up the surfaces a lot more than my 16 times, meaning you can create any arbitrary surface at any location relative to the charge and the flux will be the same.
#science
source
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