1 / 22

Law of Electrical Force Charles-Augustin Coulomb (1785)

" The repulsive force between two small spheres charged with the same sort of electricity is in the inverse ratio of the squares of the distances between the centers of the spheres". q 1. q 2. r. Law of Electrical Force Charles-Augustin Coulomb (1785). MKS Units: r in meters q in Coulombs

ponce
Download Presentation

Law of Electrical Force Charles-Augustin Coulomb (1785)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. " The repulsive force between two small spheres charged with the same sort of electricity is in the inverse ratio of the squares of the distances between the centers of the spheres" q1 q2 r Law of Electrical ForceCharles-Augustin Coulomb(1785)

  2. MKS Units: rin meters qin Coulombs in Newtons is a unit vector pointing from 1 to 2 The force from 1 acting on 2 1 = 9 · 109 N-m2/C2  4 We call this group of constants “k” as in: 0 What We CallCoulomb's Law q1 q2 • This force has same spatial dependence as the gravitational force, BUT there is NO mention of mass here!! • The strength of the force between two objects is determined by the charge of the two objects, and the separation between them.

  3. F (magnitude) increases • What happens if q1changes sign ( + - )? • The direction of is reversed • What happens if rincreases? q1 q2 Coulomb Law Qualitative r • What happens if q1increases? F (magnitude) decreases

  4. A charged ball Q1 is fixed to a horizontal surface as shown. When another massive charged ball Q2 is brought near, it achieves an equilibrium position at a distance d12directly above Q1. When Q1 is replaced by a different charged ball Q3, Q2 achieves an equilibrium position at distance d23 (< d12) directly above Q3. Q2 Q2 d23 d12 g Q3 Q1 1a: A) The charge of Q3 has the same sign of the charge of Q1 B) The charge of Q3 has the opposite sign as the charge of Q1 C) Cannot determine the relative signs of the charges of Q3 & Q1 1b: A) The magnitude of charge Q3 < the magnitude of charge Q1 B) The magnitude of charge Q3 > the magnitude of charge Q1 C) Cannot determine relative magnitudes of charges of Q3 & Q1

  5. Q2 Q2 Q1 • A charged ball Q1 is fixed to a horizontal surface as shown. When another massive charged ball Q2 is brought near, it achieves an equilibrium position at a distance d12directly above Q1. • When Q1 is replaced by a different charged ball Q3, Q2 achieves an equilibrium position at distance d23 (< d12) directly above Q3. d12 d23 g Q3 1a: A) The charge of Q3 has the same sign of the charge of Q1 B) The charge of Q3 has the opposite sign as the charge of Q1 C) Cannot determine the relative signs of the charges of Q3 & Q1 • To be in equilibrium, the total force on Q2 must be zero. • The only other known (from 111) force acting on Q2 is its weight. • Therefore, in both cases, the electrical force on Q2 must be directed upward to cancel its weight. • Therefore, the sign of Q3 must be the SAME as the sign of Q1

  6. Q2 Q2 Q1 • A charged ball Q1 is fixed to a horizontal surface as shown. When another massive charged ball Q2 is brought near, it achieves an equilibrium position at a distance d12directly above Q1. • When Q1 is replaced by a different charged ball Q3, Q2 achieves an equilibrium position at distance d23 (< d12) directly above Q3. d12 d23 g Q3 1b: A) The magnitude of charge Q3 < the magnitude of charge Q1 B) The magnitude of charge Q3 > the magnitude of charge Q1 C) Cannot determine relative magnitudes of charges of Q3 & Q1 • The electrical force on Q2 must be the same in both cases … it just cancels the weight of Q2 . • Since d23 < d12 , the charge of Q3 must be SMALLER than the charge of Q1 so that the total electrical force can be the same!!

  7. Gravitational vs. Electrical Force F F q1 m1 q2 m2 r ® q q 1 1 2 F = 1 elec pe r 2 4 0 pe 4 F q q elec 1 2 0 m m 1 2 = F m m G F = G grav 1 2 grav r 2 For an electron: ® F + 42 * |q| = 1.6 ´ 10-19 C elec = ´ 4 . 17 10 F m = 9.1 ´ 10-31 kg grav * smallest charge seen in nature!

  8. Notation For Vectors and Scalars r r ˆ ˆ Vector quantities are written like this :F,E,x,r To completely specify a vector, the magnitude (length) and direction must be known. The magnitude of is ; this is a scalar quantity The vector can be broken down into x, y, and z components: For example, the following equation shows specified in terms of ,q1,q2, andr : Where Fx,Fy,andFz(thex,y, andzcomponents ofF) are scalars. A unit vector is denoted by the caret “^”. It indicates only a direction and has no units.

  9. Vectors: an Example q1and q2 are point charges,q1 = +2mC and q2 = +3 mC. q1is located at and q2 is located at Find F12(the magnitude of the force of q1on q2). y(cm) q2 3 2 1 r q1 1 2 3 4 x (cm) To do this, use Coulomb’s Law: Now, plug in the numbers. F12= 67.52 N

  10. Vectors: an Example continued y(cm) q2 3 2 1 r q q1 1 2 3 4 x (cm) Symbolically Now plug in the numbers Fx = 47.74 N Fy = 47.74 N Now, find FxandFy, the x and y components of the force of q1 onq2.

  11. What is the force on qwhen both q1and q2are present?? The answer: just as in mechanics, we have theLaw of Superposition: The TOTAL FORCE on the object is just the VECTOR SUM of the individual forces. +q1 ® F 1 q ® F +q2 ® F 2 ® ® ® F = F + F 1 2 What happens when youconsider more than two charges? • If q1 were the only other charge, we would know the force on q due to q1. • If q2 were the only other charge, we would know the force on q due to q2.

  12. Two balls, one with charge Q1= +Q and the other with charge Q2 = +2Q, are held fixed at a separation d= 3R as shown. +Q Q2 Q1 3R +Q Q1 Q3 Q2 2R R (a) The force on Q3 can be zero if Q3 is positive. (b) The force on Q3 can be zero if Q3 is negative. (c) The force on Q3 can never be zero, no matter what the (non-zero!) charge Q3 is. +2Q +2Q • Another ball with (non-zero) charge Q3 is introduced in between Q1 and Q2at a distance = R from Q1. • Which of the following statements is true?

  13. +Q Q2 Q1 3R +Q Q1 Q3 Q2 (a) The force on Q3 can be zero if Q3 is positive. 2R R (b) The force on Q3 can be zero if Q3 is negative. (c) The force on Q3 can never be zero, no matter what the (non-zero) charge Q3 is. • Two balls, one with charge Q1= +Qand the other with charge Q2 = +2Q, are held fixed at a separation d= 3Ras shown. • Another ball with (non-zero) charge Q3 is introduced in between Q1 and Q2 at a distance = R from Q1. • Which of the following statements is true? The magnitude of the force on Q3due toQ2is proportional to (2QQ3 /(2R)2) The magnitude of the force onQ3due toQ1is proportional to (QQ3 /R2) These forces can never cancel, because the force Q2 exerts on Q3 will always be 1/2 of the force Q1 exerts on Q3!!

  14. What is the force acting onqo() ? y (cm) 4 3 2 1 qo q1 q q2 1 2 3 4 5 x(cm) We have What areF0xandF0y? Decompose into its x andycomponents Another Example qo, q1, and q2 are all point charges where qo = -1mC, q1 = 3mC, and q2 = 4mC.Their locations are shown in the diagram.

  15. y (cm) 4 3 2 1 qo Now add the components of and to find and q1 q2 1 2 3 4 5 x(cm) Another Example continued qo, q1, and q2 are all point charges where qo = -1mC, q1 = 3mC, and q2 = 4mC.Their locations are shown in the diagram.

  16. y (cm) 4 3 2 1 qo q1 q2 Let’s put in the numbers . . . 1 2 3 4 5 x(cm) The magnitude of is Another Example continued qo, q1, and q2 are all point charges where qo = -1mC, q1 = 3mC, and q2 = 4mC.Their locations are shown in the diagram.

  17. Electric field, introduction What is a Field? A FIELD is something that can be defined anywhere in space • A field represents some physical quantity • (e.g., temperature, wind speed, force) • It can be a scalar field (e.g., Temperature field) • It can be a vector field (e.g., Electric field) • It can be a “tensor” field (e.g., Space-time curvature) One problem with the above simple description of forces is that it doesn’t describe the finite propagation speed of electrical effects. In order to explain this, we must introduce the concept of the electric field.

  18. A Scalar Field 72 73 77 75 71 82 77 84 68 80 64 73 83 82 88 55 66 88 80 75 88 90 83 92 91 These isolated temperatures sample the scalar field (you only learn the temperature at the point you choose, but T is defined everywhere (x, y)

  19. A Vector Field 72 73 77 75 71 82 77 84 68 80 64 73 83 56 55 57 66 88 80 75 88 90 83 92 91 It may be more interesting to know which way the wind is blowing... It may be more interesting to know which way the wind is blowing… That would require a vector field (you learn both wind speed and direction)

  20. ® ® ® F = F + F 1 2 Summary • Charges come in two varieties • negative and positive • in a conductor, negative charge means extra mobile electrons, and positive charge means a deficit of mobile electrons • Coulomb Force • bi-linear in charges • inversely proportional to square of separation • central force • Law of Superposition • Fields

  21. Suppose your friend can push their arms apart with a force of 100 lbs. How much charge can they hold outstretched? 2m -Q +Q Appendix A: Electric Force Example F= 100 lbs = 450 N = 4.47•10-4 C That’s smaller than one cell in your body!

  22. Coulomb’s Law gives force acting on chargeQ1 due to another charge, Q2. superposition of forces from many charges Electric field is a function defined throughout space here, Electric field is a shortcut to Force later, Electric field takes on a life of it’s own! Q2 Q1 Q3 Appendix B: Outline of physics 212

More Related