output.to from Sideway
Draft for Information Only

# Content

`Electric Field of a RingβElectric Field along axis of a RingβElectric Field along Axis of a diskβInfinity Charged PlaneβSource and Reference`

# Electric Field of a Ring

## Electric Field along axis of a Ring

The electric field πΈ at β¨0,0,π§β© with radius π due to charged particle at β¨-π,0,0β© is ```π=β¨π,0,π§β©β|π|=(π2+π§2)1/2βπ=π|π|=β¨π,0,π§β©(π2+π§2)1/2 πΈ at β¨0,0,π§β©: πΈ=14ππ0π|π|2π β=14ππ0π(π2+π§2)β¨π,0,π§β©(π2+π§2)1/2=14ππ0π(π2+π§2)3/2β¨π,0,π§β© ``` The total electric field πΈπ‘ππ‘ at β¨0,0,π§β© due to a ring of charged particles. By symmetry, the electric field πΈπ‘ππ‘ ```πΈπ‘ππ‘=βββaroundthe ringβπΈπ§π§ βπΈπ§=14ππ0π§βπ(π2+π§2)3/2``` Let total net charge π is uniformlly distributed on the ring with total length πΏ of radius π. The total electric field πΈπ‘ππ‘ at β¨0,0,π§β© is ```πΏ=2ππ; βπ=π2ππβπΏ=ππΏβπΏ βπΏ=πβπβββπΏβπ2πβ«0ππ=2ππ=πΏ ββπ=π2πππβπ=π2πβπ βββπβπ2π2πβ«0ππ βπΈπ‘ππ‘ π§=14ππ0βπ§βπ(π2+π§2)3/2β14ππ0π2π2πβ«0π§ππ(π2+π§2)3/2 β=14ππ0π2ππ§(π2+π§2)3/22πβ«0ππ β=14ππ0ππ§(π2+π§2)3/2 ```

## Electric Field along Axis of a disk

The electric field πΈ at β¨0,0,π§β© with radius π due to charged particle βπ of βA=βπβπΏ at β¨-π,0,0β© is similar to that of a ring. Let total net charge π is uniformly distributed on the disk with total area π΄ of radius π. ```Total π in area A=ππ2 Elemental βππ in area element βAπ=(ππβπ)(βπ) ββππ=πππ2βAπ=πππ2(ππβπ)(βπ) βββπβππ=ββππππ2βAπ=πππ2ββπ(ππβπβπ) β=πππ2β¬(ππππππ)=πππ2πβ«0πππ2πβ«0ππ=πππ212π22π=π βπΈπ‘ππ‘ π§=14ππ0βπ§βπ(π2+π§2)3/2β14ππ0πππ2β¬(ππππππ)π§(π2+π§2)3/2 β=14ππ0πππ2πβ«0ππ§(π2+π§2)3/2ππ2πβ«0ππ=14ππ0πππ21βπ§π2+π§22π β=12π0πππ21βπ§π2+π§2 β΄πΈπ‘ππ‘ π§=12π0πππ21βπ§π2+π§2π§ ```

## Infinity Charged Plane

Assume π go to infinity, e.g. πβ«π§ ```πββ; πββ βπππ2=π charge per unit area πΈπ‘ππ‘ π§=12π0πππ21βπ§π2+π§2π§=12π0π1β0π§=π2π0π§ ``` For two parallel opposite charged infinite plane

## Source and Reference

ID: 191102202 Last Updated: 11/22/2019 Revision: 0

Nu Html Checker 53 na na

Home 5

Management

HBR 3

Information

Recreation

Culture

Chinese 1097

English 339

Computer

Hardware 249

Software

Application 213

Latex 52

Manim 205

KB 1

Numeric 19

Programming

Web 289

Unicode 504

HTML 66

CSS 65

SVG 46

ASP.NET 270

OS 429

Python 72

Knowledge

Mathematics

Set 1

Algebra 84

Geometry 34

Calculus 67

Engineering

Mechanical

Rigid Bodies

Statics 92

Dynamics 37

Control

Natural Sciences

Electric 27