Physics 202, Lecture 2

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1 Physics 202, Lectue 2 Todays Topics Electic Foce and Electic Fields Electic Chages and Electic Foces Coulomb's Law Physical Field The Electic Field Electic Field Lines Motion of Chaged Paticle in Electic Field

2 Demo: Two Types of Electic Chages Opposite signs attact Like signs epel

3 Popeties of Electic Chages 2+1 types: positive, negative (+neutal). Unit: Coulomb (C). 1 C= chage of 6.24x10 18 potons. Electic chage is quantized: q=±ne, e=1.602x10-19 C Building blocks of mattes: Chage (C) Mass (kg) Electon -e=-1.602x x10-31 Poton +e=+1.602x x10-27 Neuton x10-27 Electic chage is conseved: chages can be moved aound, but the total chage emains the same. Fo deep thinkes: Why electons and potons have the same electic chage?

4 Electic Foce And Coulombs Law Electic foces exist between two chaged paticles The diection of electic foce depends on the signs of the chages: foces between opposite sign chages ae attactive foces between like sign chages ae epulsive The magnitude of the electic foces fo point chages F 12 = F 21 = k e q 1 q 2 2 (Coulombs Law) Coulomb Constant: k e = 8.987x10 9 Nm 2 /C 2 = 1/(4πε 0 ) ε 0 : pemitivity of fee space

5 Numeic Examples: Electic Foce Is Stong Electic foce between two 1C chages 1 mete apat: F=8.99x10 9 N Poton and electon in a hydogen atom: q electon = -1.6x10-19 C, q poton = 1.6x10-19 C, =5.3x10-11 m à Electic foce F= 8.2 x10-8 N. This foce is lage: Compaed to the mass of poton: 1.673x10-27 kg Compaed to the gavitational foces between them: F G = 3.6x10-47 N (ecall: F G =Gm 1 m 2 / 2 ) Fou fundamental foces: Stong > Electomagnetic > Weak >> Gavitational

6 Coulombs Law in Vecto Fom E. Foce on q 2 by q 1 : F F Execise: Use this vecto fom to veify the attactive/epulsive featue Note: Multiple paticles on chage i, F i = F 1i +F 2i + F 3i +. = = K K e e q q q q ˆ 12 ˆ 21 = F E. Foce on q 1 by q 2 : ˆ

7 Quick Quiz Two chages, q 1 =0.1C and q 2 =5q 1 (i.e.0.5c), ae sepaated by a distance =1m. Let F 2 denotes the foce on q 2 (exeted by q 1 ), and F 1 denotes the foce on q 1 (exeted by q 2 ). Which of the following elationship is tue? F 1 =5F 2 F 1 =-5F 2 F 2 =-5F 1 F 1 =-F 2

8 Popeties of the Electic Foce It is one of fou fundamental foces: Stong >Electomagnetic > weak >> gavity It is popotional to 1/ 2 : double à ¼ F Its diection is chage sign dependent: like signà epulsive, opposite sign à attactive It is a consevative foce. (Wok independent of path) W = i f F d = A potential enegy can be defined. (chapte 23) k k e q1q q1q e 2 U = f 2 + k e q1q i 2 = ( U f ) ( U Note the similaities and diffeences to gavity i )

9 A Vey Impotant Concept: Field What is a physical field? Field: A physical quantity which has a physical value* at each point in space (i.e. a distibution). Examples of physical fields: tempeatue, wind speed, electic field, magnetic field, In this couse, we conside only scala and vecto foms of physical quantities.

10 Example of Scala and Vecto Fields Tempeatue (scala) Wind speed (vecto) Measuement can be made at any point on the map.

11 The Coulombs Law Revisited Oiginal (Coulombs) view of electic foce: q 1 diectly applies an electic foce on q 2 q q F = K 1 2 ˆ 12 e 2 Field view of electic foce: q 1 ceates an electic field E aound it The electic field E applies a foce on q 2 12 q F = K 1 ˆ q = E q 2 e E In this field view: q 1 : souce chage q 2 : test chage E independent of q 2

12 Electic Field and Electic Foce q E = F K e = E q = Ke q 0 2 ˆ q 0 2 ˆ q q 0 q 0 : souce chage E: field by q 0 q: test chage F = qe foce on q by E 12

13 Visualization of Electic Field: Field Lines Use of field lines is a convenient way to visualize electic fields Simple ules fo dawing field lines: line diection: diection of E vecto line density: elative stength of E. (dense = lage)

14 Field Lines e.g.: Point-Like Chages Magnitude E=k e q/ 2 Magnitude E=k e q/ 2 +q -q

15 Example 2: Two Chaged Paticles +q and +q +q and - q (dipole) Each field line always stats fom a + q and end at a -q (o )

16 Motion Of Chaged Paticle In The Electic Field Fundamental Fomulas: F=qE a=f/m = qe/m v= v i +at If initially est (v i =0) then v= at = (qe/m) t Motion of +q: Same di. as E -q +q E Motion of - q: Opposite di. as E 16

17 Execise: An Electon in a Unifom E. Field Find out vetical displacement afte the electon pass though a downwad unifom electic field E Fo an electon chage e and mass m Answe: dy = - ½at 2 = = - ½(F/m) (t) 2 =- ½(eE/m) (l/v i ) 2 17

18 Execise: Electic Foces Due to Two Chaged Paticles Find the electic foce on q 3.

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