Electric Field F E. q Q R Q. ˆ 4 r r - - Electric field intensity depends on the medium! origin

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1 1 1 Electic Field + + q F Q R oigin E 0 0 F E ˆ E 4 4 R q Q R Q - - Electic field intensity depends on the medium!

2 Electic Flux Density We intoduce new vecto field D independent of medium. D E So, electic flux, D ds In SI units, one line of electic flux emntes fom +1C nd temintes on -1C. We will len moe on flux lines lte. D : Flux density C/m 0 Guss s Lw The Ide The totl electic flux though ny closed sufce is equl to the totl chge enclosed by tht sufce. d D ds S Totl chge enclosed Q v dv v A vey useful computtionl technique to find the electic field E when the souce hs enough symmety. 4

3 d D ds Fist Mxwell s Eqution S Totl chge enclosed Q By pplying divegence theoem DdS D dv S Theefoe v D v v dv Fist Mxwell s Eqution v The volume chge density is the sme s the divegence of the electic flux density. 5 Guss s Lw - Appliction Povides n esy mens of finding E o D fo symmeticl chge distibution. A continuous chge distibution my hve the following symmety: 1. Rectngul symmety it depends only on x (o y o z). Cylindicl symmety it depends only on (independent of nd z). Spheicl symmety it depends only on (independent of nd ). Whethe the chge distibution is symmetic o not, Guss s lw lwys holds! 6

4 Guss s Lw - Appliction 1. Identify whethe symmety exists.. Choose Gussin sufce S.. Clculte Chge enclosed by sufce S Apply Guss s Lw Q S D ds 7 Choosing Gussin Sufce Q S D ds Tue fo ALL sufces. Useful (to clculte D ) fo SOME sufces. D is noml to the sufce. D ds D ds o - D ds D is tngentil to the sufce. D ds 0 8 4

5 Symmety & Gussin Sufces Souce Symmety Spheicl Cylindicl Pln Gussin Sufce Concentic Sphee Coxil Cylinde Gussin Pillbox 9 Identify symmety spheicl D is eveywhee noml to the Gussin sufce D D ˆ Point Chge Choose Gussin sufce A spheicl sufce centeed t the oigin z D P Q y x 10 5

6 Identify symmety spheicl Point Chge Choose Gussin sufce A spheicl sufce centeed t the oigin D is eveywhee noml to the Gussin sufce D D ˆ Apply Guss s Lw Q D ds D ds D 4 D Q 4 ˆ x z D P Q y Gussin sufce 11 Infinite Line Chge Identify symmety cylindicl Choose Gussin sufce A D cylindicl sufce with xis long the line is eveywhee constnt nd noml to the Gussin sufce D D ˆ P D 1 6

Infinite Line Chge Identify symmety cylindicl Choose Gussin sufce A D cylindicl sufce with xis long the line is eveywhee constnt nd noml to the Gussin sufce D D ˆ l P D Apply Guss s Lw l Q L D d S D

7 Infinite Line Chge Identify symmety cylindicl Choose Gussin sufce A D cylindicl sufce with xis long the line is eveywhee constnt nd noml to the Gussin sufce D D ˆ l P D Apply Guss s Lw l Q L D d S D ds D l L D ˆ Gussin sufce 1 Infinite Sheet of Chge Identify symmety pln Choose Gussin sufce A D ectngul box o Gussin Pillbox is eveywhee constnt nd noml to the Gussin sufce D D z ˆ z Infinite sheet of Chge S C/m z D Ae A y x D Gussin sufce 14 7

8 Apply Guss s Lw Infinite Sheet of Chge S ds Q D ds D z ds ds top bottom S A Dz ( A A) z Infinite sheet of S D ˆ Chge z S C/m D Ae A y x D Gussin sufce 15 Unifomly Chged Sphee Identify symmety spheicl Choose Gussin sufce A spheicl sufce centeed t the oigin D is eveywhee noml to the Gussin sufce D D ˆ Gussin sphee 16 8

9 Unifomly Chged Sphee Region 1: Dw Gussin sphee in egion 1 ( ) Note: is bity but is the dius fo which you will clculte the D! Gussin sphee 17 Region 1: Unifomly Chged Sphee Q vdv v dv v sin d d d v DdS D ds D sin d d 0 0 D 4 Apply Guss s Lw 4 D 4 v D ˆ, 0 v Gussin sphee 18 9

10 Unifomly Chged Sphee Region : > Dw Gussin sphee in egion 1 ( > ) Agin: Remembe tht is bity but is the dius fo which you will clculte D! Gussin sphee 19 Unifomly Chged Sphee Region : > Q vdv v dv v sin d d d v DdS D 4 Apply Guss s Lw 4 D 4 v D ˆ, v Gussin sphee 0 10

11 Unifomly Chged Sphee D v 0 v v 1 Concept Question: Flux The electic flux though the pln sufce below (positive unit noml to left) is 1. Positive. Negtive. Zeo 4. None of the bove. 11

12 Concept Question: Flux thu Sphee The totl flux though the spheicl sufce is 1. Positive (net outwd flux). Negtive (net inwd flux). Zeo 4. None of the bove. Concept Question: Chge in Pymid A pymid hs sque bse of side, nd fou fces which e equiltel tingles. A chge Q is plced on the cente of the bse of the pymid. Wht is the net electic flux emeging fom one of the tingul fces of the pymid? Q/8. Q / 4. Q/ 5. Undetemined: we must know whethe Q is infinitesimlly bove o below the plne? 4 1

13 Concept Question: Slb of Chge Conside positive, semi-infinite (in x nd y) flt slb z-xis is pependicul to the sheet, with cente t z = 0. At the plne s cente (z = 0), E field 1. Points in the positive z-diection. Points in the negtive z-diection. Points in some othe (x, y) diection 4. Is zeo 5. Cnnot be detemined. 5 Concept Question: Spheicl Shell We just sw tht in solid sphee of chge the electic field gows linely with distnce. Inside the chged spheicl shell t ight ( < ) wht does the electic field do? 1. Constnt nd Zeo. Constnt but Non-Zeo. Still gows linely 4. Some othe functionl fom (use Guss s Lw) 5. Cn t detemine with Guss s Lw Q 6 1

14 Clss Test 1 Dte: August 014 Time: 1 pm Syllbus: Lectues

General Physics II. number of field lines/area. for whole surface: for continuous surface is a whole surface

General Physics II. number of field lines/area. for whole surface: for continuous surface is a whole surface Genel Physics II Chpte 3: Guss w We now wnt to quickly discuss one of the moe useful tools fo clculting the electic field, nmely Guss lw. In ode to undestnd Guss s lw, it seems we need to know the concept