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Induced charge distribution of metallic sphere. Feng lei. What is a chromatic image supposed to be ?. M ×N. A colorized image is a matrix which has a dimension of 3 ×M ×N , and the index of which represents corresponding pixel.
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What is a chromatic image supposed to be ? M ×N A colorized image is a matrix which has a dimension of 3 ×M ×N , and the index of which represents corresponding pixel. Each M ×N matrix is supposed to be a color element matrix of the image in RGB color space.
RGB color space A specified color has three elements: ZR (0,1) ZG (0,1) ZB (0,1) To illustrate the density of charge by color, we have to define a spectrum of these colors first.
There are many ways to make a color band. I only choose one plane (ZR-ZB) of RGB color space to define my spectrum.
How to convert induced charge density to color distribution ? The simplest way is to find a linearrelation between them. Then I get that k must be the maximum of σ.
How will R/d change the relative density ? R/d varying in the scope of (0.1,0.9) and θ∈(-Pi , Pi).
What dose it look like in the mapping plane? x-y y-z R/d=0.1 R/d=0.3 R/d=0.7
What about the condition near the limit point ? R/d=0.9 R/d=0.99 Those induced charges just appears locating on one point.
Let’s do something more interesting! How about adding another two point charges outside the metallic sphere? R/d=0.4
How about adding two negative point charges outside the metallic sphere? R/d=0.4
How about just changing the distance of the point charge outside the metallic sphere? R/d=0.3 R/d=0.7
Y-Z Finally, here are two interesting graphs mapped in y-z plane. Can you guess how the point charges locate?
Thanks for your attention! It is wrong but gorgeous anyway.