Induced charge distribution of metallic sphere Feng lei

What is a chromatic image supposed to be ? 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. M ×N

RGB color space A specified color has three elements: Z R (0,1) Z G (0,1) Z B (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 (Z R -Z B ) of RGB color space to define my spectrum.

How to convert induced charge density to color distribution ? The simplest way is to find a linear relation 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? R/d=0.1R/d=0.3R/d=0.7 x-y y-z

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=0.7 R/d=0.3

Finally, here are two interesting graphs mapped in y-z plane. Can you guess how the point charges locate? Y-Z

Actually, it’s the situation below:

Thanks for your attention! It is wrong but gorgeous anyway.