Electricity and Magnetism Coulomb s Law

Transcription

1 Electricity and Magnetism Coulomb s Law Lana Sheridan De Anza College Jan 10, 2018

2 Last time introduced charge conductors insulators induced charge

3 Warm Up. Do both balloons A and B have a charge? ntry by entering the ds each other e another ge opposite type charged (A) yesor (B) no, neither is charged (C) at least 1 is charged. ns being

4 Warm Up. Do both balloons A and B have a charge? ntry by entering the ds each other e another ge opposite type charged (A) yesor (B) no, neither is charged (C) at least 1 is charged. ns being

5 charged or Warm Up Does this happen? straight t. e identical ther and both (A) yes (B) no

6 charged or Warm Up Does this happen? straight t. e identical ther and both (A) yes (B) no consider Newton s 3rd law

7 Overview Force from a point charge Quantization of charge Charge conservation

8 Electrostatic Forces For a pair of point-particles with charges q 1 and q 2, the magnitude of the force on each particle is given by Coulomb s Law: F 1,2 = k e q 1 q 2 r 2 k e is the electrostatic constant and r is the distance between the two charged particles. k e = 1 4πɛ 0 = N m 2 /C 2

9 How Coulomb s Law was found: Torsion Balance 694 Chapter 23 Electric Fields Suspension head 23.3 Coulomb s L Charles Coulomb measured objects using the torsion ba Fiber ciple of the torsion balance to measure the density of t spheres replaced by charge and B in Figure 23.5 causes resulting motion causes the of the twisted fiber is prop measurement of this angle attraction or repulsion. On between them is very large gravitational force can be n From Coulomb s experi B force (sometimes called th A ticles. We use the term po The electrical behavior of e them as point charges. Fro Figure 23.5 Coulomb s balance, tude of the electric force ( 1 Figure from Serway & Jewett, Physics for Scientists and Engineers, 9th ed.

10 Electrostatic Forces: Coulomb s Law F 1,2 = k e q 1 q 2 r 2 Remember however, forces are vectors. The vector version of the law is: F 1 2 = k e q 1 q 2 r 2 ˆr 1 2 where F 1 2 is the force that particle 1 exerts on particle 2, and ˆr 1 2 is a unit vector pointing from particle 1 to particle 2.

11 Coulomb s Law Coulomb s Law: F 1 2 = k q 1q 2 r 2 ˆr 1 2 Does this look a bit familiar? Similar to this? F 1 2 = G m 1m 2 r 2 ˆr 1 2

12 Coulomb s Law ric Fields F 1 2 = k q 1q 2 r 2 ˆr 1 2 When the charges are of the same sign, the force is repulsive. When the charges are of opposite signs, the force is attractive. r rˆ 12 q 2 S F 12 S F 21 S F 12 q 2 S F 21 q 1 q 1 a b same sign 1 as Figure in Figure from Serway 23.6a, & the Jewett, product Physics q 1 q 2 for is positive Scientists and andthe Engineers, electric 9th force ed. on one

13 Electrostatic Constant The electrostatic constant is: k = 1 4πɛ 0 = N m 2 C 2 ɛ 0 is called the permittivity constant or the electrical permittivity of free space. ɛ 0 = C 2 N 1 m 2

14 12 Example The diagram a shows two positively charged particles fixed in place on the x axis.the charges are q 1 = C and q 2 = C, and the particle separation is R = m. What are the magnitude This and direction is the first of the electrostatic force 1-8 (a) F 2 1 from particle 2 on particle 1? arged particharges q 1 are fixed in n an x axis. e free-body m for particle F 12 q 1 arrangement. R (a) k = N m 2 C 2 or ɛ 0 = C 2 N 1 m 2 ing the elecic force on it article 2. (c) q 2 This is the particle of interest. 1 Question from Halliday, Resnick, Walker, 9th ed x x F 12 q 1 This arra F

15 12 Example The diagram a shows two positively charged particles fixed in place on the x axis.the charges are q 1 = C and q 2 = C, and the particle separation is R = m. What are the magnitude This and direction is the first of the electrostatic force 1-8 (a) F 2 1 from particle 2 on particle 1? F 12 q 1 arrangement. R (a) Answer: F 2 1 = i N arged particharges q 1 are fixed in n an x axis. e free-body m for particle ing the elecic force on it article 2. (c) q 2 This is the particle of interest. 1 Question from Halliday, Resnick, Walker, 9th ed x x F 12 q 1 This arra F

16 Force from many charges Forces from many charges add up to give a net force This is (very grandly) called the principle of superposition. The net force on particle 1 from particles 2, 3,... n is: F net,1 = F F F n 1

17 nt is true about the electric forces on the objects? Example S B 52F S BA (c) 3 S FAB 52F S BA (d) S FAB 5 3 S FBA F BA Consider three point charges located at the corners of a right triangle as shown, where q 1 = q 3 = 5.00 µc, q 2 = 2.00 µc, and a = m. Find the resultant force exerted on q 3. riangle as shown in m. Find the q 2 y a S F 23 S F 13 q 3 arge q 3 is near two s are exerted in difhown in the figure, a 2a q 1 x tegorize this examq 1 and q 2 on q 3 are force exerted by q 2 on q 3 is S 1 F Figure 23.7 (Example 23.2) The force exerted by q 1 on q 3 is S F13. The Figure from Serway & Jewett, pg 696, S Ex

18 B 52F S BA (c) 3 S FAB 52F S BA (d) S FAB 5 3 S F S BA Example F BA Consider three point charges located at the corners of a right triangle as shown, where q 1 = q 3 = 5.00 µc, q 2 = 2.00 µc, and a = m. Find the resultant force exerted on q 3. riangle as shown in m. Find the q 2 y a S F 23 S F 13 q 3 arge q 3 is near two s are exerted in difhown in the figure, a 2a q 1 x tegorize this examq 1 and q 2 on q 3 are force exerted by q 2 on q 3 is S F23. 1 Figure from Serway The & resultant Jewett, pg force 696, S F3 Ex exerted 2. on q Figure 23.7 (Example 23.2) The Answer: F force exerted by q 1 on q 3 is S net,3 = ( 1.04 i j) N F13. The 3 S S

19 Question R/2 +8Q (c) articles. p pg 574, #10, HRW (3) (4) Fig Question In Fig , a central particle of charge 2q is surrounded by a square array of charged particles, separated by either distance d or d/2 along the perimeter of the square. What are the magnitude and direction of the net electrostatic force on the central particle due to the other particles? (Hint: Consideration of symmetry can greatly reduce the amount of work required here.) d +2q 7q +4q e 5q 3q e +3q 2q d 3q 5q e +4q 7q +2q

20 Forces at a Fundamental Level Often people think about two kinds of forces: contact forces and field forces (ie. forces that act at a distance). In mechanics problems, all forces except gravity are from direct contact. Gravity is a field force. The electric and magnetic forces are also field forces.

21 Forces at a Fundamental Level Often people think about two kinds of forces: contact forces and field forces (ie. forces that act at a distance). In mechanics problems, all forces except gravity are from direct contact. Gravity is a field force. The electric and magnetic forces are also field forces. And actually, at a fundamental level, all forces that we know of are field forces.

22 Forces at a Fundamental Level Contact forces are a result of electrostatic repulsion at very small scales.

23 Forces at a Fundamental Level Contact forces are a result of electrostatic repulsion at very small scales. Fundamental forces: Force Rel. strength Range (m) Attract/Repel Carrier Gravitational attractive graviton Electromagnetic 10 2 attr. & rep. photon Weak Nuclear < attr. & rep. W +, W, Z 0 Strong Nuclear 1 < attr. & rep. gluons

24 Forces at a Fundamental Level Contact forces are a result of electrostatic repulsion at very small scales. Fundamental forces: Force Rel. strength Range (m) Attract/Repel Carrier Gravitational attractive graviton Electromagnetic 10 2 attr. & rep. photon Weak Nuclear < attr. & rep. W +, W, Z 0 Strong Nuclear 1 < attr. & rep. gluons

25 Forces at a Fundamental Level Contact forces are a result of electrostatic repulsion at very small scales. Fundamental forces: Force Rel. strength Range (m) Attract/Repel Carrier Gravitational attractive graviton Electromagnetic 10 2 attr. & rep. photon Weak Nuclear < attr. & rep. W +, W, Z 0 Strong Nuclear 1 < attr. & rep. gluons Gravity is actually quite a weak force, but it is the only one that (typically) matters on large scales - charges cancel out!

26 Fields field (physics) A field is any kind of physical quantity that has values specified at every point in space and time.

27 Vector Fields In EM we have vector fields. The electrostatic force is mediated by a vector field. vector field (physics) any kind of physical quantity that has values specified as vectors at every point in space and time. vector field (math, 3 dimensions) A vector field is a vector-valued function F that takes a point (x, y, z) and maps it to a vector F(x, y, z).

28 Fields Fields were first introduced as a calculation tool. A force-field can be used to identify the force a particular particle will feel at a certain point in space and time without needing a detailed description of the other objects in its environment that it will interact with.

29 Fields Fields were first introduced as a calculation tool. A force-field can be used to identify the force a particular particle will feel at a certain point in space and time without needing a detailed description of the other objects in its environment that it will interact with. Imagine a charge q 0. We want to know the force it would feel if we put it at a specific location.

30 Fields Imagine a charge q 0. We want to know the force it would feel if we put it at a specific location. The electric field E at that point will tell us that! F = q 0 E Charges (source of E-field) Environment Field System +q F E Charges (source of E-field)

31 Fields Charges (source of E-field) Environment Field System +q F E Charges (source of E-field) The source of the field could be another charge or charges, but we do not need a description of the sources of the field to describe what their effect is on our particle. All we need to know is the field! (This is also true for gravity. We do not need the mass of the Earth to know something s weight.)

32 Vector Fields 2 - dimensional examples Irrotational (curl-free) field.

33 Vector Fields 2 - dimensional examples Solenoidal (divergence-free) field.

34 Summary Force from a point charge Force from many charges vector fields Quiz Friday, start of class. Homework Collected homework 1, posted online, due on Monday, Jan 22. Serway & Jewett: Read Ch 23 Ch 23, onward from page 716. Conceptual Qs: 5; Section Qs: 11, 13