复旦大学：《电动力学》学生课堂报告_金属球上感应电荷分布的课堂报告

Induced charge distribution of metallic sphere Feng lei

Induced charge distribution of metallic sphere Feng lei

q z d q xy平面 1 rd q 4丌a r(r=R R R R 2-COS(0) 4R2 d

2 3 2 2 2 ( ) 0 1 1 2 ( ) 4 − =          −      +                −      = −   =      Cos d R d R d R d R R q r r R         = − − q q r R d r q 1 / 4 0 

What is a chromatic image supposed to be ■ M×N A colorized image is a matrix which has a dimension of3×M×N,and the index of which represents piXel corresponding pixel R Each M XNmatrix is supposed to be a color element matrix of the image in RGB color space

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 Blue A specified color has three Fuchsin White elements Black (01) Green zG(0,1 0,1) Red To illustrate the density of charge by color, we have to define a spectrum of these colors first

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

0.75 B R 0.5 There are many ways to make a color band. i only choose one plane(Zr-ZB)of rGB color space to define 0.25 my spectrum

There are many ways to make a color band. I only choose one plane (ZR -ZB ) of RGB color space to define my spectrum. 0.4 1 ZB = − ZR

How to convert induced charge density to color distribution The simplest way is to find a linear relation between them kZ Then i get that k must be the maximum of o max R R R 2-CoS(0) max

How to convert induced charge density to color distribution ? The simplest way is to find a linear relation between them. R  = kZ Then I get that k must be the maximum of σ. = ZR  max  2 3 3 2 max 1 1 2 ( ) −          −      +       = −    Cos d R d R d R

How will R/d change the relative density 0.1 0.2 366个 0 R/d varying in the scope of (0. 1,0.9 )and 0E(-Pi, pi)

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? y R/d=01 R/d=03 R/d=07

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=09 R/d=099 Those induced charges just appears locating on one point

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! outside the metallicsphere o point charges How about adding another ty sphere y-Z R/d=04

Let’s do something more interesting! How about adding another two point charges outside the metallic sphere? R/d=0.4