Theme Music: MGMT Electric Feel* Cartoon: Bob Thaves Frank & Ernest

Transcription

1 Octobe7, 013 Physics 131 Pof. E. F. Redish Theme Music: MGMT Electic Feel* Catoon: Bob Thaves Fank & Enest 1 Foothold ideas: Chage A hidden popety of matte Matte is made up of two kinds of electical matte (positive and negative) that usually cancel vey pecisely. Like chages epel, unlike chages attact. Binging an unbalanced chage up to neutal matte polaizes it, so both kinds of chage attact neutal matte The total amount of chage (pos neg) is constant. 3 Pof. E. F. Redish 1

2 Foothold ideas: Conductos and Insulatos Insulatos In some matte, the chages they contain ae bound and cannot move aound feely. Excess chage put onto this kind of matte tends to just sit thee (like speading peanut butte). Conductos In some matte, chages in it can move aound thoughout the object. Excess chage put onto this kind of matte edistibutes itself o flows off (if thee is a conducting path to gound). 4 Foothold idea: Coulomb s Law All objects attact each othe with a foce whose magnitude is given by Q = " F Qq = k CqQ qq k C is put in to make the units come out ight. k C = N-m / C ˆ qq 5 Pof. E. F. Redish

3 Making Sense of Coulomb s Law Changing the test chage Changing the souce chage Changing the distance Specifying the diection Intepet the sign F Qq = " Q = k C qq R ˆ Qq 6 Quantifying Chage Need an opeational definition. Chage is a new kind of quantity (to M, L, T, add Q). Choose ou scale: A small object has a chage of 1 C ( = 1 Coulomb) if two identical such chages held at a distance of 1 m exet foces of 9 x 10 9 N on each othe. This coesponds to choosing the constant k C = 9 x 10 9 N-m /C. 7 Pof. E. F. Redish 3

4 Adding foces fo many chages = F Q1 q + F Q q + F Q3 q + F Q4 q +... = k CqQ 1 " 1 + k CqQ whee = distance fom Q 1 to q = distance fom Q to q... " + k CqQ 3 " 3 + k CqQ " = diection fom Q 1 to q (mag. 1, no units) = diection fom Q to q (mag. 1, no units) 8 Review of Vectos (-dimensional coodinates) We have diections to specify. We must Choose a efeence point (oigin) Pick pependicula axes (x and y) Choose a scale We specify ou x and y diections by dawing little aows of unit length in thei positive diection. iˆ, ˆj A foce vecto is witten F = F iˆ + F ˆj = F, F x y ( ) 9 x y Pof. E. F. Redish 4

5 Adding Foces We define the sum of two vectos as if they wee successive displacements. F F 1 + F = 1 F F F 10 Adding Vectos: Methods Thee ae 3 mathematical ways to add vectos head paallelogam add components to tail ule (may use tig) 11 Pof. E. F. Redish 5

6 Tig eview The atios of a tiangle s sides only depend on θ. sin(θ) = opposite/hypotenuse cos(θ) = adjacent/hypotenuse tan(θ) = opposite/adjacent. 13 Vectos with tig by components A = A x î + A y ĵ = ( Acos() )î + ( Asin() ) ĵ B = B x î + B y ĵ = ("Bsin(#))î + ( Bcos(#) ) ĵ A + B =? 14 Pof. E. F. Redish 6

7 Foothold ideas: Electic Foces and Fields When we focus ou attention on the electic foce on a paticula chage (a test chage) we see the foce it feels factos into the magnitude of its chage times a facto that depends on position (and the othe chages). 1 Foothold ideas: Fields A field is a concept we use to descibe anything that vaies in space. It is a set of values assigned to each point in space (e.g., tempeatue o wind speed). A foce field is an idea we use fo non-touching foces. It puts a foce vecto at each point in space, summaizing the effect of all objects that would exet a foce on a paticula object placed at that point. A gavitational, electic, o magnetic field is a foce field with something (a coupling stength ) divided out so the field no longe depends on what test object is used. g = F acting on m m E = F acting on q q Field is the value at a position in space assuming that the foce is measued by placing the object at. Pof. E. F. Redish 7

8 Making sense Notice that E = /q does NOT depend on q Fo one souce chage = k qq C 1 " 1 Fo many souces = k qq C 1 " 1 + k qq C " + k qq C 3 " E = Fq E = q = k Q C 1 q = k Q C 1 " " + k Q C " + k Q C 3 " Pof. E. F. Redish 8