induced charge distribution of metallic sphere feng lei
TRANSCRIPT
Induced charge distribution of metallic sphere
Feng lei
2
322
2
)(0
)(2114
Cosd
R
d
R
d
R
d
R
R
q
r Rr
qq r
dR
r
q /1
4 0
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.
B
G
R
Z
Z
Z
M ×N
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.
4.01 RB ZZ
How to convert induced charge density to color distribution ?The simplest way is to find a linear relation between them.
RkZ
Then I get that k must be the maximum of σ.
RZmax
2
323
max
)(211
Cosd
R
d
R
d
R
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=0.1 R/d=0.3 R/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.