1. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Conservation of energy Work and Delta PE Electric potential energy Electric potential Contour Maps E-Field and Equipotential Conductors & Fields Capacitance Chapter 21 Electric Potential Topics: Sample question: Shown is the electric potential measured on the surface of a patient. This potential is caused by electrical signals originating in the beating heart. Why does the potential have this pattern, and what do these measurements tell us about the heart’s condition? Slide 21-1

2. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Chapter 21 Key Energy Equations Key Energy Equations from Physics 151 and Ch. 21 so far Definition of Work Where Work done by a conservative force (F g, F s, & F e ) Also work done by conservative force is path independent => W ext = - W e Conservation of Energy Equation (can ignore U g and U s unless they are relevant) Electric Energy – Special Cases (Similar equations for gravity) 2 Point Charges Charge in a Uniform E-field Note: in both cases of Electric Energy must assume where U e = 0 Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

3. Chapter 21 Key Equations (3) Key Points about Electric Potential Electric Potential is the Electric Energy per Charge Electric Potential increases as you approach positive source charges and decreases as you approach negative source charges (source charges are the charges generating the electric field) A line where  V= 0 V is an equipotential line (The electric force does zero work on a test charge that moves on an equipotential line and  PE e = 0 J) For multiple source charges V POI = V 1@POI + V 2@POI + … Slide 21-16 Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

4. Electric Potential and E-Field for Three Important Cases Slide 21-25 For a point charge For very large charged plates, must use

5. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric field of a charged conductor Free electrons in a conductor are quickly redistributed until equilibrium is reached, at which point the E field inside the conductor and parallel to its surface becomes zero.

6. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric field outside a charged conductor

7. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Grounding Grounding discharges an object made of conducting material by connecting it to Earth. Electrons will move between and within the spheres until the V field on the surfaces of and within both spheres achieves the same value.

8. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. What is Q 2 ? Example Problem Slide 21-35

9. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Uncharged conductor in an electric field: Shielding The free electrons inside the object become redistributed due to electric forces, until the E field within the conducting object is reduced to zero.

10. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Uncharged conductor in an electric field: Shielding The interior is protected from the external field—an effect called shielding.

11. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Dielectric materials in an electric field If an atom in a dielectric material resides in a region with an external electric field, the nucleus and the electrons are displaced slightly in opposite directions until the force that the field exerts on each of them is balanced by the force they exert on each other.

12. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Polar water molecules in an external electric field Some molecules, such as water, are natural electric dipoles even when the external E field is zero.

13. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. E field inside a dielectric A dielectric material cannot completely shield its interior from an external electric field, but it does decrease the field.

14. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. E field inside a dielectric Physicists use a physical quantity to characterize the ability of dielectrics to decrease the E field: The dielectric constant κ

15. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Dielectric constants for different types of materials

16. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric force and dielectrics The force that object 1 exerts on object 2 is reduced by κ compared with the force it would exert in a vacuum. Inside the dielectric material, Coulomb's law is now written as:

17. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Salt dissolves in blood but not in air When salt is placed in water or blood: Many more collisions occur between molecules than between molecules and air; these can break an ion free from the crystal. Any ions that become separated do not exert nearly as strong as an attractive force on each other because of the dielectric effect. The random kinetic energy of the liquid is sufficient to keep the sodium and chlorine ions from recombining, allowing the nervous system to use the freed sodium ions to transmit information.

18. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Tip

19. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Capacitors A capacitor consists of two conducting surfaces separated by a nonconducting material. Charges on the two conductors must have charges with equal magnitude and opposite sign. The role of a capacitor is to store electric energy (AKA Electric Potential Energy U e ).

20. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Capacitors (Cont'd)

21. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Capacitors If we consider the capacitor plates to be large flat conductors, charge should be distributed evenly on the plates. The magnitude of the E field between the plates relates to the potential difference from one plate to the other and the distance separating them To double the E field, the charge on other plates has to double.

22. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Capacitors The proportionality constant C in this equation is called the capacitance of the capacitor. The unit of capacitance is 1 coulomb/volt = 1 farad (in honor of Michael Faraday).

23. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Capacitance of a capacitor A capacitor with larger-surface-area plates should be able to maintain more charge separation because there is more room for the charge to spread out.

24. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Capacitance of a capacitor A larger distance between the plates leads to a smaller-magnitude E field between the plates. Because the magnitude of this E field is proportional to the amount of electric charge on the plates, a larger plate separation leads to a smaller-magnitude electric charge on the plates.

25. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Capacitance of a capacitor Material between the plates with a large dielectric constant becomes polarized by the electric field between the plates. Thus more charge moves onto capacitor plates that are separated by material of high dielectric constant.

26. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Capacitance of a capacitor The capacitance of a particular capacitor should increase if the surface area A of the plates increases, decrease if the distance d between them is increased, and increase if the dielectric constant k of the material between them increases:

27. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Tip

28. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Energy of a charged capacitor To determine the electric potential energy in a charged capacitor, we start with an uncharged capacitor and then calculate the amount of work that must be done on the capacitor to move electrons from one plate to the other.

29. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Energy of a charged capacitor The process of charging a capacitor is similar to stretching a spring: at the beginning, a smaller force is needed to stretch the spring by a certain amount compared to the much greater force needed when the spring is already stretched.

30. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Lightning When the E field in air or in some other material is very large, free electrons accelerate and quickly acquire enough kinetic energy to ionize atoms and molecules in their path when colliding with them.

31. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Lightning rods Dielectric breakdown occurs between the cloud and the lightning rod. Drawing lightning to the rod and away from the building prevents damage to the building and its inhabitants.

32. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Magnets and the magnetic field Electric currents create magnetic fields Magnetic fields of wires, loops, and solenoids Magnetic forces on charges and currents Magnets and magnetic materials Chapter 24 Magnetic Fields and Forces Topics: Sample question: This image of a patient’s knee was made with magnetic fields, not x rays. How can we use magnetic fields to visualize the inside of the body? Slide 24-1

33. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Key Points Three types of magnetic interactions 1.no interaction with either pole of a magnet => object is non-magnetic 2.attracted to both poles of a magnet => object is magnetic 3.Attracted to one pole and repelled by the other pole => object is a magnet Magnetic field vector from a bar magnet is a super position of the magnetic field vectors from the N and S poles: Vector from N pole points away from N pole Vector from S pole points towards S pole Field lines form complete loops inside and outside of magnet Field lines outside magnet go from N to S poles Field lines inside magnet go from S to N poles Magnetic Field vectors at a point are tangential to Magnetic Field Lines

34. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 3-D Arrows, Cross Products, and Right Hand Rule 1 Slide 24-2 Showing vectors in 3D (need this for magnetic force) Cross Product For direction use Right-hand rule 1 Right-hand rule 1 (RHR 1) => for finding direction of cross-product vector (Cross-Product Rule) 1.Point right hand in the direction of the first vector (vector A) 2.Rotate your right hand until you can point your fingers in the direction of the second vector (vector B) 3.Thumb points in direction the cross-product vector (vector C)

35. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Right Hand Rules for Magnetism Right-hand rule 1 (RHR 1) => for finding magnetic force F B = q*v_vector x B_vector (Cross-Product Rule) 1.Point right hand in the direction the charges are moving (current or velocity) 2.Rotate your right hand until you can point your fingers in the direction of the magnetic Field 3.Thumb points in direction of force for + charge Force is in opposite direction for - charges Right-hand rule 2 (RHR 2) => Finding direction of B from I Point thumb of right hand in direction of current I, B-field lines curl in direction of fingers Right-hand rule 3 (RHR 3) => Finding direction of current in a loop from direction of B-field Point thumb of right hand in direction of B-field Fingers of right hand curl in direction of current Slide 24-2

36. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Electric Currents Also Create Magnetic Fields A long, straight wire A current loopA solenoid Slide 24-15

37. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Drawing Field Vectors and Field Lines of a Current-Carrying Wire Slide 24-21

38. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The Magnitude of the Field due to a Long, Straight, Current-Carrying Wire Slide 24-25

39. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Drawing a Current Loop Slide 24-22

40. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The Magnetic Field of a Current Loop Slide 24-23

41. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The Magnetic Field of a Current Loop Magnetic field at the center of a current loop of radius R Magnetic field at the center of a current loop with N turns Slide 24-29

42. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The Magnetic Field of a Solenoid A short solenoidA long solenoid Slide 24-24

43. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The Magnetic Field Inside a Solenoid Magnetic field inside a solenoid of length L with N turns. Slide 24-31

44. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Body cells as capacitors Cells, including nerve cells, have capacitor-like properties. The conducting "plates" are the fluids on either side of a moderately nonconducting cell membrane. In this membrane, chemical processes cause ions to be "pumped" across the membrane. As a result, the membrane's inner surface becomes slightly negatively charged, while the outer surface becomes slightly positively charged.

45. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Cell Capacitance Example Estimate: 1. The capacitance C of a single cell. 2. The charge separation q of all of the membranes of the human body's 10 13 cells. Assume that each cell has a surface area of A = 1.8 x 10 −9 m 2, a membrane thickness of d = 8.0 x 10 −9 m, ΔV = 0.070 across the membrane wall, and a membrane dielectric constant κ = 8.0.

46. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Quantitative Exercise Estimate the capacitance of your physics textbook, assuming that the front and back covers (area A = 0.050 m 2, separation d = 0.040 m) are made of a conducting material. The dielectric constant of paper is approximately 6.0. Determine what the potential difference must be across the covers for the textbook to have a charge separation of 10 −6 C (one plate has charge +10 −6 C and the other has charge −10 −6 C).

47. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Energy of a charged capacitor To determine the electric potential energy in a charged capacitor, we start with an uncharged capacitor and then calculate the amount of work that must be done on the capacitor to move electrons from one plate to the other.

48. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Energy of a charged capacitor The process of charging a capacitor is similar to stretching a spring: at the beginning, a smaller force is needed to stretch the spring by a certain amount compared to the much greater force needed when the spring is already stretched.

49. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Quantitative Exercise In Example 15.10, we estimated that the total charge separated across all the cell membranes in a human body was about 11 C. Recall that the potential difference across the cell membranes is 0.070 V. Estimate the work that must be done to separate the charges across the membranes of the body's approximately 10 13 cells.