Coulomb s Law and Electric Fields

Transcription

1 Physics 102: Lecture 02 Coulomb s Law and Electric Fields Today we will get some practice using Coulomb s Law learn the concept of an Electric Field Physics 102: Lecture 2, Slide 1

2 4 m Coulomb Law practice: Three Charges Calculate force on +2mC charge due to other two charges Draw forces Calculate force from +7mC charge Calculate force from 7mC charge dd (VECTORS!) Q=+2.0mC F +7 F -7 Q=+7.0mC 6 m Q=-7.0 mc Physics 102: Lecture 2, Slide 2

3 4 m Three Charges Calculate forces Calculate force on +2mC charge due to other two charges Draw forces Calculate force from +7mC charge Calculate force from 7mC charge dd (VECTORS!) Calculate magnitudes F = k q 1q 2 r 2 Q=+2.0mC F +7 F +7 = F -7 F 7 = = N Q=+7.0mC 6 m Q=-7.0 mc Physics 102: Lecture 2, Slide 3

4 4 m Three charges dding Vectors F +7 +F -7 Calculate components of vectors F +7 and F -7 : F +7,x = F +7 cos θ = N 3 5 F +7 F +7,y = F +7 sin θ = N 4 5 Q=+2.0mC F 7,x = F 7 cos θ = N 3 5 F -7 F 7,y = F 7 sin θ = N 4 5 Q=+7.0mC 6 m Q=-7.0 mc Physics 102: Lecture 2, Slide 4

5 4 m Three charges dding Vectors F +7 +F -7 dd like components of vectors F +7 and F -7 : F x = F +7,x + F 7,x = N F y = F +7,y + F 7,y = 0 Final vector F has magnitude and direction Q=+2.0mC F +7 F F = F x 2 + F y 2 = N F -7 φ = tan 1 F y F x = 0 Q=+7.0mC 6 m Q=-7.0 mc Double-check with drawing Physics 102: Lecture 2, Slide 5

6 Electric Field Charged particles create electric fields. Direction is the same as for the force that a + charge would feel at that location. Magnitude given by: E F/q = kq/r 2 Q p =1.6x10-19 C + r = 1x10-10 m E E = ( )( )/(10-10 ) 2 N = N/C (to the right) Physics 102: Lecture 2, Slide 6

7 CheckPoint 1.1 What is the direction of the electric field at point? 1) Up 2) Down 3) Left 4) Right 5) Zero y B x Physics 102: Lecture 2, Slide 7

8 CT: E Field What is the direction of the electric field at point C?. Left B. Right C. Zero y C B x Physics 102: Lecture 2, Slide 8

9 4 m E Field from 2 Charges Calculate electric field at point due to two unequal charges Draw electric fields Calculate E from +7mC charge Calculate E from 3.5mC charge dd (VECTORS!) Note: this is similar to (but a bit harder than) my earlier example. We ll do some of this here you try the rest at home! Q = +7.0mC 6 m Q = 3.5 mc Physics 102: Lecture 2, Slide 9

10 4 m E Field from 2 Charges Calculate electric field at point due to charges Calculate E from +7mC charge Calculate E from 3.5mC charge dd* E = k q/r 2 E 7 = )( E 7 = N/C E 3 = )( E 3 = N/C N/C N/C Q=+7.0mC 6 m E 7 E 3 Q=-3.5 mc Physics 102: Lecture 2, Slide 10

11 4 m dding Vectors E 7 +E 3 Decompose into x and y components. E 7x = E 7 cos(θ) = E = N/C E 7y = E 7 sin(θ = E = N/C E 7 q E 7x E 7y =E 7 (3/5) =E 7 (4/5) q Q=+7.0mC 6 m Q=-3.5 mc Physics 102: Lecture 2, Slide 11

12 4 m dding Vectors E 7 +E 3 Decompose into x and y components. dd components. E 7x = N/C E 7 E 3x = N/C E 7y = N/C E total E 3y = N/C E 3 E x = N/C E y = N/C Physics 102: Lecture 2, Slide 12 6 m Q=+7.0mC Q=-3.5 mc E = E 2 2 x + E y = N/C

13 Comparison: Electric Force vs. Electric Field Electric Force (F) the force felt by a charge at some location Electric Field (E) found for a location only (any location) tells what the electric force would be if a + charge were located there: F = Eq Both are vectors, with magnitude and direction. Ok, what is E actually good for? Physics 102: Lecture 2, Slide 13

14 Electric fields: useful record-keeping tool! calculate once for fixed charges, use to find force on other charges (like ions/electrons in neurons, heart tissue, and cell membranes) Physics 102: Lecture 2, Slide 14 Eisenberg, BU

15 Electric Field Map Electric field defined at any location (you did three:, B, C) y C B x Physics 102: Lecture 2, Slide 15

16 Electric Field Lines Closeness of lines shows field strength (lines never cross) Number of lines at surface Q rrow gives direction of E (Start on +, end on ) Physics 102: Lecture 2, Slide 16 This is becoming a mess!!!

17 CheckPoint 2.1 X Y B Charge is 1) positive 2) negative 3) unknown Physics 102: Lecture 2, Slide 17

18 CheckPoint 2.2 / CT X X Y Y B B Compare the ratio of charges Q / Q B 1) Q = 0.5Q B 2) Q = Q B 3) Q = 2 Q B Physics 102: Lecture 2, Slide 18

19 CheckPoint 2.3 X Y B The magnitude of the electric field at point X is greater than at point Y 1) True 2) False Physics 102: Lecture 2, Slide 19

20 E inside of conductor Conductor electrons free to move Electrons feels electric force - will move until they feel no more force (F=0) F=Eq: if F=0 then E=0 E=0 inside a conductor (lways!) Physics 102: Lecture 2, Slide 20

21 Demo: E-field from dipole y C B x Physics 102: Lecture 2, Slide 21

22 Recap E Field has magnitude and direction: E F/q Calculate just like Coulomb s law Careful when adding vectors Electric Field Lines Density gives strength (# proportional to charge.) rrow gives direction (Start + end on ) Conductors Electrons free to move E = 0 Physics 102: Lecture 2, Slide 22