Class 2. Lesson 1 Stationary Point Charges and Their Forces. Basic Rules of Electrostatics. Basic Rules of Electrostatics

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1 Lesson 1 Stationay Point Chages and Thei Foces Class Today we will: lean the basic chaacteistics o the electostatic oce eview the popeties o conductos and insulatos lean what is meant by electostatic induction ind out why static electostatic oces ae usually attactive discuss the poblem o oce at a distance lean the basics o two types o models that eplain why thee ae oces Basic Rules o Electostatics Basic Rules o Electostatics Chages come in two types: positive and negative. Positive chage is poduced on a glass od by ubbing it with silk o plastic. Negative chage is poduced on a ubbe od by ubbing it with u. Like chages epel, unlike chages attact. Conductos ae mateials in which chages move eely. Insulatos ae mateials in which chages emain in ied locations. Chages come in multiples o the electic chage. 19 e 1.61 C The total chage in the univese is always conseved. The oce between chages is stonge when the chages ae close. What happens when we put a chaged od nea a steam o wate? Conclusion: The steam o wate is attacted both ods. It doesn t matte i the od is positively chaged o negatively chaged. How can we undestand this?

2 Polaization In most neutal atoms o molecules, the cente o positive chage coincides with the cente o negative chage In the pesence o a chaged object, these centes may sepaate o otate slightly This esults in moe positive chage on one side o the molecule than on the othe side This ealignment o chage on the suace o an insulato is known as polaization The chaged object (on the let) induces chage on the suace o the insulato chaged comb attacts bits o pape due to polaization o the pape Eamples o Polaization The oce between the objects is attactive because the oce is stonge between close chages. Eamples o Polaization How does an electophous wok? Chages in the conducting plate become polaized. Chages on the insulating plate emain whee they wee. Electons om you inge low into the plate, neutalizing the top suace

3 Negative chage edistibutes itsel on the metal plate. When you touch it again, electons low o the plate into you inge. Physics and Tuth s physicists, we deal with models. Models equie 1) symbols and ) ules o manipulating symbols. These symbols and ules have a 1-to-1 coespondence with natue. Physicists can say elatively little about tuth at a undamental level. So is light a wave o a paticle? sometimes it acts like a wave sometimes it acts like a paticle light is neithe wave no paticle -- it s light. ction at a distance. ction at a distance. action = oce I the eath is 93,, miles om the sun, how does it know it should be attacted to the sun? We equently use two vey dieent models o theoies to eplain action at a distance. Remembe that both ae models, and neithe is tuth.

4 Vitual Paticle Theoies Vitual Paticle Theoies chages constantly emit and eabsob vitual paticles that cay enegy and momentum. i anothe chage absobs the vitual paticle, a oce is eeted. Vitual Paticle Theoies Geometical Theoies electomagnetic oce: QED quantum electodynamics +weak oce: electoweak theoy stong oce: QCD quantum chomodynamics matte modiies the cuvatue o space-time. cuved space-time aects the motion o matte. Geometical Theoies gavity: Geneal Relativity + electomagnetic oce: KK Kaluza-Klein Theoies in 5-dimensional space. Thee Models o Electomagnetic Foces Thead Model: Descibes the inteactions between point chages. Tells why oces behave as they do. Field Lines: Easy way to visualize oces between collections o chages. Mawell s Equations: mathematical vesion o ield lines.

5 Class 3 Today we will: lean how the thead model descibes the oce between point chages at est constuct Coulomb s law om the thead model lean how to use Coulomb s law to calculate the oce between chages at est Thead Model valid ecept in quantum mechanical egime. helps us undestand the elationship between electicity and magnetism. gives quantitative esults. useul o visualizing oces, adiation, magnetic ields. Thead Model Field paticle Feels oce Thead Model Field paticle Feels oce Souce paticle Causes oce Souce paticle Causes oce We will only daw the theads o the souce chage! Thead Model When a souce paticle is at est, it emits theads isotopically and in huge numbes. Theads have a head (solid cicle) and a tail (open cicle). I this ails to load, cut and paste the URL. + Thead Model Theads ae vey shot. Theads tavel at the speed o light adially outwad.

6 Thead Model Theads point away om positive souces and towad negative souces. Theads ae not modiied by the pesence o chages. Thead Model Remembe that the theads always tavel adially outwad! I this ails to load, cut and paste the URL. Thead Model Thead Model Foce Foce To ind the oce on a chage embedded in a sea o theads, all we need to do is look at a snapshot theads. I the chage is positive, the oce is in the diection o the theads. It doesn t matte how the theads ae moving! I the chage is negative, the oce is opposite the diection o the theads. Thead Model souce chages ield chages The oce on positive ield chages is in the diection o the theads. The oce on negative ield chages is opposite the diection o the theads. Foce Foce Foce + Foce Thead Model Theads cay no enegy o momentum. They eet a oce by modiying space nea a ield paticle. To calculate the oce on a ield paticle, we need to know: The chage o the ield paticle. The density o theads nea the ield paticle. The length o the theads. The diection o the theads.

7 Thead Model F e q Thead Model F e q constants Thead Model F e q chage o the ield paticle F Thead Model e q thead vecto: gives the length and diection o the theads F Thead Model e q thead density: gives the numbe o theads pe unit volume Finding the Foce e F q We know eveything but (nu), the density o theads. But i we know how many theads ae emitted pe second, we can detemine how many theads thee ae pe unit volume anywhee in space!

8 The Numbe o Theads in a Shell In the tet, we ound the numbe o theads in a spheical shell and the volume o the shell. Dividing these gives us the density. d Coulomb s Law 1 F 4 q s q ˆ Coulomb s Law In pactice, it s easie to change this just a little: 1 qsq F 4 1 qsq 3 4 ˆ 1 qsq 4 ˆ Shot Vecto Review Magnitude =, diection = Unit vectos: ˆ, yˆ, ˆ, ˆ Components: ˆ yˆ, cos, y, y y tan y y sin Shot Vecto Review B Dot poduct: B B yby z Bz B cos Coss poduct: B Bsin nˆ ( ight hand ule) ˆ yˆ zˆ B B y y B z z Finding the Foce 1 F 4 To calculate a oce, we need: is a constant q s is the chage o the souce paticle usually given q is the chage o the ield paticle usually given q q is the vecto om the souce to the ield paticle s 3

9 +3C (m, 3m) n eample: C (7m, 1m) Rule o Units I you put eveything in SI units The esult is in SI units! Red: at (m, 3m), chage is +3C. Blue: at (7m, 1m), chage is 4C. What is the oce on the blue chage? 5ˆ yˆ n eample: +3C (, 3) C (7, 1) qsq F ˆ yˆ F N F Nˆ Nyˆ 9 3 5ˆ yˆ N Which Foce Fomula Do I Use? It s all the same thing, but sometimes one is easie to use than the othe. I all you need is the magnitude: F qsq 1 4 qsq 1 I is in a simple diection - F I ˆ ˆ : 4 qsq I is moe complicated: F 4 goes om the souce to the ield chage. 3 ˆ Class 4 Today we will: eview the meaning o potential enegy ind the potential enegy o point chages at est wok some potential enegy poblems Potential Enegy something we invent so enegy can be conseved only good o oces whee the wok aound a closed path is zeo. W F d

10 Potential Enegy and Foce The geneal elation is: Patial Deivatives (, y) 3 y 3y F U U U ˆ y U yˆ z zˆ 6y 3y but we ll stick to simple poblems. y 3 6y Potential Enegy and Foce Fo a oce in the diection: U F, U ( ) Fo a oce in the diection: U F, U ( ) Fd Fd Gavity F mg U ( y) mg dy mgy C Fdy F mg, Gavity U ( y) Fdy mgy C The constant C is abitay. We can t eve measue U at a point, we can only measue the change in U! stonomical Gavity GMm F U ( ) Fd GMm d 1 GMm 1 GMm C

11 stonomical Gavity GMm F, U ( ) GMm Fd C In this case, the convenient choice o C is zeo, so the potential enegy is zeo when the bodies ae vey a apat. GMm U ( ) C C stonomical Gavity GMm U ( ) Since G, M, m, and must be positive: U() Objects tend to move to lowe potential enegy, which means the oce is towad smalle. The Electostatic Foce 1 F 4 U ( ) We again choose C to be zeo. Notice the sign is positive. q q s 1 Fd 4 q s q The Electostatic Foce I one chage is positive and the othe chage is negative: U() U ( ) 1 4 The oce is towad smalle, so it is attactive. q q s The Electostatic Foce I both chages have the same sign: U() U ( ) 1 4 The oce is towad lage, so it is epulsive. q q s Electostatic Potential Enegy U ( ) 1 4 qsq In a hydogen atom, the aveage distance o the electon om the poton is m. Estimate the enegy it take to emove the electon om the atom. = = (1.6 1 ) J= J (This is twice the actual ionization enegy because we ignoed the initial kinetic enegy.)

12 Electostatic Potential Enegy The chages, each o 1. C ae placed as shown. What is the potential enegy o the chage at the oigin? 1.cm = J= J Whee is the potential enegy =? Does the diection o the chages matte? 1.cm Electostatic Potential Enegy The chages, each o 1. C ae placed as shown. What is the TOTL potential enegy o the system o chages? 1.cm = J J =.44 J cm 1.41cm