1. Lecture Outline Chapter 16 College Physics, 7 th Edition Wilson / Buffa / Lou © 2010 Pearson Education, Inc.

2. The Why?? X-rays Heart Defibrillators Nervous System

3. 16.1 Electric Potential Energy and Electric Potential Difference The simplest electric field pattern is between 2 large, oppositely charged plates. (How do we calculate electric field?) Let’s talk about each picture… Work Formula is…

4. 16.1 Electric Potential Energy and Electric Potential Difference It takes work to move a charge against an electric field. Just as with gravity, this work increases the potential energy of the charge. To find the change in potential energy you use the formula below: Why is this the same equation as Work? © 2010 Pearson Education, Inc.

5. 16.1 Electric Potential Energy and Electric Potential Difference Just as with the electric field, it is convenient to define a quantity that is the electric potential energy per unit charge. This is called the electric potential difference. Unit of electric potential difference: the volt, V Which is the same thing as J/C © 2010 Pearson Education, Inc.

6. 16.1 Electric Potential Energy and Electric Potential Difference The potential difference between parallel plates can be calculated relatively easily: For a pair of oppositely charged parallel plates, the positively charged plate is at a higher electric potential than the negatively charged one by an amount Δ V. © 2010 Pearson Education, Inc.

7. 16.1 Electric Potential Energy and Electric Potential Difference Imagine a moving proton from a negative to positive plate. The plates are 1.5 cm apart and the field is 1500 N/C. –a.) What is the change in electric potential energy? –b.) What is the electric potential difference –c.) If the proton is released from rest at the positive plate, what speed will it have just before it hits negative plate?

8. 16.1 Electric Potential Energy and Electric Potential Difference Potential differences are defined in terms of positive charges, as is the electric field. Therefore, we must account for the difference between positive and negative charges. Positive charges, when released, accelerate toward regions of lower electric potential. Negative charges, when released, accelerate toward regions of higher electric potential. © 2010 Pearson Education, Inc.

9. 16.1 Electric Potential Energy and Electric Potential Difference Modern dental offices use X- ray machines for diagnosing different problems. To do this, electrons are accelerated through electric potential differences (voltage) of 25,000 V. When the electrons hit the positive plates, the kinetic energy is converted into a photon. Suppose a single electron’s kinetic energy is distributed equally among 5 photons. How much energy would one photon have?

10. 16.1 Electric Potential Energy and Electric Potential Difference In non-uniform fields, the field strength can vary. This diagram shows the electric potential difference of a point charge. © 2010 Pearson Education, Inc.

11. 16.1 Electric Potential Energy and Electric Potential Difference Whether the electric potential increases or decreases when towards or away from a point charge depends on the sign of the charge. Electric potential increases when moving nearer to positive charges or farther from negative charges. Electric potential decreases when moving farther from positive charges or nearer to negative charges. © 2010 Pearson Education, Inc.

12. 16.1 Electric Potential Energy and Electric Potential Difference The electric potential at a distance from a point charge can be calculated using the following formula: V = kq r Where k = 9.0 x 10 9 N m 2 /C 2

13. 16.1 Electric Potential Energy and Electric Potential Difference According to the Bohr Model of the hydrogen atom, the smallest orbit has a radius of 0.0529 nm, and the next largest radius has a radius of 0.212 nm. a.) How do the values of the electric potentials at each orbit compare: –1.) the smaller orbit is at a higher potential –2.) the larger is at a higher potential –3.) they have the same potential b.) Verify your answer by calculating the electric potentials.

14. 16.1 Electric Potential Energy and Electric Potential Difference The electric potential energy of a system of two charges is the change in electric potential multiplied by the charge. © 2010 Pearson Education, Inc.

15. 16.1 Electric Potential Energy and Electric Potential Difference The additional potential energy due to a third charge is the sum of its potential energies. © 2010 Pearson Education, Inc.

16. 16.1 Electric Potential Energy and Electric Potential Difference Water is a permanent polar molecule. The distance from each H atom to the O atom is 9.60 x 10-11m, and the angle between the two H-O bonds is 104 degrees. What is the total electrostatic energy of the water molecule.

17. 16.2 Equipotential Surfaces and the Electric Field An equipotential surface is one on which the electric potential does not vary. This means the potential is the same. If the charge is moved perpendicular to the electric field, then it takes no work to move a charge along an equipotential surface. Why would there be no work? © 2010 Pearson Education, Inc.

18. 16.2 Equipotential Surfaces and the Electric Field Equipotentials are analogous to contour lines on a topographic map. © 2010 Pearson Education, Inc.

19. 16.2 Equipotential Surfaces and the Electric Field Equipotentials are always perpendicular to electric field lines. This enables you to draw one if you know the other. © 2010 Pearson Education, Inc.

20. 16.2 Equipotential Surfaces and the Electric Field Here, these principles have been used to draw the electric field lines and equipotentials of an electric dipole. © 2010 Pearson Education, Inc

21. 16.2 Equipotential Surfaces and the Electric Field The potential difference between any 2 equipotential planes is found by: ΔV = EΔx The direction of the electric field E is that in which the electric potential decreases the most rapidly. [Draw a pic] Its magnitude at maximum rate is given by: © 2010 Pearson Education, Inc.

22. 16.2 Equipotential Surfaces and the Electric Field Under normal atmospheric conditions, the Earth’s surface is electrically charged. This creates an approximately constant electric field of about 150 V/m pointing down near the surface. a.) Under these conditions, what is the shape of the equipotential surfaces, and in what direction does the electric potential decrease most rapidly? b.) How far apart are two equipotential surfaces that have a 1000V difference between them? Which has a higher potential, the one farther from Earth or closer?

23. 16.2 Equipotential Surfaces and the Electric Field A solid conductor with an excess positive charge is shown to the left. Which of the following best describes the shape of the equipotential surfaces just outside the conductor’s surface: a.) Flat planes b.) Spheres c.) The shape of the conductor’s surface © 2010 Pearson Education, Inc.

24. 16.2 Equipotential Surfaces and the Electric Field The electron-volt (eV) is the amount of energy needed to move an electron through a potential difference (voltage) of one volt. The electron-volt is a unit of energy, not voltage, and is not an SI standard unit. It is, however, quite useful when dealing with energies on the atomic scale. © 2010 Pearson Education, Inc.

25. 16.3 Capacitance A pair of parallel plates will store electric energy if charged; this arrangement is called a capacitor. This energy storage occurs because it takes work to transfer charge between the plates. © 2010 Pearson Education, Inc.

26. 16.3 Capacitance A battery does the work of removing electrons electrons from the positive plate and transfer (or pump) them through a wire to the negative plate. As a result: a separation of charge occurs and an electric field will be created. The battery will continue to charge the capacitor until the voltage between the plates is the same as the battery. –When disconnected from the battery, the capacitor becomes a storage reservoir of electric energy.

27. 16.3 Capacitance The charge is related to the potential difference. Capacitance represents the amount of charge stored per volt. SI unit of capacitance: the farad, F Larger capacitance = more energy/charge stored. © 2010 Pearson Education, Inc.

28. 16.3 Capacitance For a parallel-plate capacitor, The quantity inside the parentheses is called the permittivity of free space, and is represented by ε 0. © 2010 Pearson Education, Inc. C = ε o A d

29. 16.3 Capacitance What would be the plate area of an air filled 1.0 F parallel plate capacitor if the plate separation were 1.0 mm?

30. 16.3 Capacitance The energy stored in a capacitor is equal to the work done by the battery. This energy can be found 3 different ways. © 2010 Pearson Education, Inc.

31. 16.3 Capacitance During a heart attack, the heart can beat in an erratic fashion, called fibrillation. One way to get it back to normal rhythm is to shock it with electrical energy supplied by a cardiac defibrillator. About 300J of energy is required to produce the desired effect. Typically a defibrillator stores this energy in a capacitor charged by a 5000V power supply. a.) What capacitance is required? b.) What is the charge on the capacitor’s plates?

32. SKIPPING YO! Skipping Dielectrics because will not be tested on AP Exam. This is all of Section 16.4

33. 16.5 Capacitors in Series and in Parallel Capacitors can be connected in two basic ways: –Series: capacitors are connected head to tail. –Parallel: all the leads on one side of the capacitors have a common connection. (all heads together, or all tails together) –Let’s look at each of these separately.

34. 16.5 Capacitors in Series and in Parallel Let’s draw capacitors in a series configuration. Capacitors in series all have the same charge. Q 1 = Q 2 = Q 3 The total potential difference is the sum of the potentials across each capacitor. V total = V 1 + V 2 + V 3 The total voltage would be the same as the source of the voltage. So for example… © 2010 Pearson Education, Inc.

35. 16.5 Capacitors in Series and in Parallel The equivalent series capacitance (C s ) is defined as the value of a single capacitor that could replace the series combination and store the same charge and energy at the same voltage. What the what? Let’s draw a picture. Cs is always the smallest capacitance in the series. The smallest capacitance in a series receives the largest voltage.

36. 16.5 Capacitors in Series and in Parallel Let’s draw capacitors in a parallel configuration. Capacitors in parallel all have the same potential difference (same voltage). V 1 = V 2 = V 3 The total charge is the sum of the charge on each. Q total = Q 1 + Q 2 + Q 3 The capacitance (C p ) is found by: C p is larger than the largest capacitance. © 2010 Pearson Education, Inc.

37. 16.5 Capacitors in Series and in Parallel We can picture capacitors in parallel as forming one capacitor with a larger area: © 2010 Pearson Education, Inc.

38. 16.5 Capacitors in Series and in Parallel Given two capacitors, one with a capacitance of 2.50 μF, and the other with that of 5.00 μF, what are the charges on each and the total charge stored if they are connected across a 12.0 V battery –a.) in series –b.) in parallel

39. 16.5 Capacitors in Series and in Parallel 3 capacitors are connected in a circuit shown to the right. –a.) By looking at the capacitance values, how do the voltages across the capacitors compare? V 3 > V 2 > V 1 V 3 < V 2 = V 1 V 3 = V 2 = V 1 V 3 = V 2 > V 1 –b.) Determine the voltages across each capacitor. –c.) Determine the stored energy in each capacitor. This is considered a difficult problem!