Physics 122B Electricity and Magnetism

1. Physics 122B Electricity and Magnetism Lecture 12 (Knight: 30.1 to 30.4) Calculating E from V April 23, 2007 Martin Savage

2. Lecture 12 Announcements • Lecture HW Assignments #4 has been posted on the Tycho system. Assignment #4 is due at 10 PM, on Wednesday. • Requests for regrades of Exam 1 should be written on a separate sheet (see Syllabus) and taken to Heleb Gribble in room C136 PAB. They will be accepted until noon on Wednesday. Physics 122B - Lecture 12

3. Chapter 29 – Summary (1) Physics 122B - Lecture 12

4. Chapter 29 – Summary (2) Physics 122B - Lecture 12

5. The Missing Link How are E and V connected? Physics 122B - Lecture 12

6. Finding V from E Physics 122B - Lecture 12

7. Potential from the Fieldof a Point Charge This is the same result that we obtained in Chapter 29 from energy considerations. Physics 122B - Lecture 12

8. Example:The Potential of a Charged Disk Physics 122B - Lecture 12

9. Finding E from V In other words, the E field components are determined by how much the potential V changes in the three coordinate directions. Physics 122B - Lecture 12

10. Example:The E Field of a Charged Ring Physics 122B - Lecture 12

11. Example:Finding E from the Slope of V An electric potential V in a particular region of space where E is parallel to the x axis is shown in the figure to the right. Draw Ex vs x. Physics 122B - Lecture 12

12. Question Which graph of the electric potential V describes the electric field shown? Physics 122B - Lecture 12

13. Geometry of Potential and Field Physics 122B - Lecture 12

14. Example: Finding the E-Field from Equipotential Surfaces The figure shows a contour map of a potential. Estimate the strength and direction of the electric field at points 1, 2, and 3. ~ Physics 122B - Lecture 12

15. Kirchhoff’s Loop Law Since the electric field isconservative, any path betweenpoints 1 and 2 finds the same potential difference. Any path can be approximated by segments parallel and perpendicular to equipotential surfaces, and the perpendicular segments must cross the same equipotentials. Since a closed loop starts and ends at the same point, the potential around the loop must be zero. This is Kirchhoff’s Loop Law, which we will use later. Physics 122B - Lecture 12

16. Question Which set of equipotential contours describes the electric field shown? Physics 122B - Lecture 12

17. A Conductor inElectrostatic Equilibrium A conductor is in electrostatic equilibrium if all charges are at rest and no currents are flowing. In that case, Einside=0. Therefore, all of it is at a single potential: Vinside=constant. Rules for conductor. Physics 122B - Lecture 12

18. Sources of Electric Potential A potential difference can be created by moving charge from one conductor to another. The potential difference on a capacitor can produce a current (flow of charge), but this current cannot be sustained because the charge separation and potential difference rapidly disappears. Physics 122B - Lecture 12

19. The Van de Graaff Generator • A Van de Graaff Generator“pumps” charge on a movingbelt, creating a large potential difference. • Charge is mechanicallytransported from the negativeside to the positive side and sustains a potential differencebetween the spherical domeelectrode and its surroundings. • The electric field of the dome exerts a downward force on the positive charges moving up the belt, causing the belt motor to do increasing work as the system charges. The work goes into “lifting” the positive charges through the rising field. Physics 122B - Lecture 12

20. Batteries and EMF A battery is a chemical source of electric potential difference. Chemical reactions create potential difference by moving positive ions to one electrode and negative ions to the other. The system can be visualized as a chemical “charge escalator” in which positive charges are “lifted” through a potential difference. The potential difference DVbat is determined by the chemistry of the electrodes (e.g., carbon and zinc) and remains essentially constant until the chemicals are exhausted and the battery is “dead”. The term EMF (electromotive force),symbol E, is used to describe the work done per unit charge by the battery: E = Wchem/q = DVbat. A real battery has “internal resistance” that increases as the chemicals are used and limits current flow. Physics 122B - Lecture 12

21. E Fields and Pointed Objects On conductors, mobile charge tends to accumulate at locations having the greatest curvature. This creates very strong electric fields near the tip of a pointed object. If such an object is negatively charged, electrons may be “field emitted” from the sharp point. Physics 122B - Lecture 12

22. Capacitors and Capacitance Capacitance Physics 122B - Lecture 12

23. 1.0 mF 1.5 V .05 mm Example: Charging a Capacitor • The spacing between the plates of a 1.0 mF capacitor is 1 mm. • What is the surface area A of the plates? • How much charge is on the plates if this capacitor is attached to a 1.5 V battery? Physics 122B - Lecture 12

24. Forming a Capacitor Any two conductors can form a capacitor, regardless of their shape. The capacitance depends only on the geometry of the conductors, not on their present charge or potential difference. (In fact, one of the conductors can be moved to infinity, so the capacitance of a single conductor is a meaningful concept.) Physics 122B - Lecture 12

25. Example: A Spherical Capacitor A metal sphere of radius R1 is inside and concentric with a hollow metal sphere of inner radius R2. What is capacitance of this spherical capacitor? Physics 122B - Lecture 12

26. Combining Capacitors Parallel: Same DV, but different Qs. Series: Same Q, but different DVs. Physics 122B - Lecture 12

27. I Rnet Rnet Reminder: Combining Resistors Conducting material that carries current across its length can form a resistor,a circuit element characterized by anelectrical resistance R:R ≡rL/Awhere L is the length of the conductor and A is its cross sectional area. R has units of ohms. Multiple resistors may be combined in series, where resistances add, or in parallel, where inverse resistances add. Physics 122B - Lecture 12

28. Example: A Capacitor Circuit Find the charge and potential difference across each capacitor shown in the figure. Physics 122B - Lecture 12

29. Energy Stored in a Capacitor Physics 122B - Lecture 12

30. End of Lecture 12 • Before the next lecture, read Knight, sections 30.6 and 30.7. • Lecture HW Assignments #4 has been posted on the Tycho system. Assignment #4 is due at 10 PM, on Wednesday . • Requests for regrades of Exam 1 should be written on a separate sheet (see Syllabus) and taken to Helen Gribble in room C136 PAB. They will be accepted until noon on Wednesday. Physics 122B - Lecture 12