Electricity & Magnetism Lecture 18 muratseyit/E1/Getty Images Today’s Concepts: - Electric Potential Energy - Electric Potential - Capacitors Presentation Created by Dr. Adam Lark Electric Field and Forces Review Force Vector! kQ q F= 2 r Electric Field kQ E= 2 r Only works between multiple charges r Q q By dividing by the charge, we have information about all space! ο² οΆ F EοΊ q Electric Potential and Electric Potential Energy Electric Potential Energy Not a Vector! kq1q2 Uelectric = r Electric Potential kQ V= r Only works between multiple charges r q1 q2 By dividing by the charge, we have information about all space! U Vº q Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Figure 17-4, Page 719 Electric Potential Energy 1 When two positive point charges move toward each other, the value of the electric potential energy Uelectric A. decreases. B. increases. C. stays the same. kq1q2 Uelectric = r Electric Potential Energy 2 When two positive point charges move away from each other, the value of the electric potential energy Uelectric A. decreases. B. increases. C. stays the same. kq1q2 Uelectric = r Electric Potential Energy 3 When two positive point charges move in such a way that the distance between then remains the same, the electric potential energy Uelectric A. decreases B. increases kq1q2 Uelectric = C. stays the same r r stays the same U stays the same Electric Potential Energy 4 When two negative point charges move toward each other, the value of the electric potential energy Uelectric A. decreases. B. increases. C. stays the same. kq1q2 Uelectric = r Electric Potential Energy 5 Which situation has the most positive electric potential energy? πΌπ ~ − π πΌπ ~ − π πΌπ ~π πΌπ ~π kq1q2 Uelectric = r 3 × −3 πA ~ 3 6 × −3 πB ~ 2 3 × 4 πC ~ 3 −2 × −3 πD ~ 2 Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Unnumbered Art, Page 721 Electric Field and Electric Potential Energy DUelectric = -qEdcosq Change in electric potential energy for a charge moving through uniform electric field for a distance at an angle. Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Figure 17-5, Page 721 Electric Potential Energy Conservation of energy still true on this scale. kq1q2 Uelectric = r K = mv 1 2 2 r q1 q2 v Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Unnumbered Art, Page 717 Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Unnumbered Art, Page 726 Electric Field and Electric Potential DV = -Edcosq Change in electric potential moving through a uniform electric field for a distance at an angle. Electric Potential 1 When a positive point charge moves in the direction of an electric field π¬, the value of the electric potential V A. decreases. π¬ B. increases. C. stays the same. Q π«π½ = −π¬ π πππ π½ π«π½ = negative! π Electric Potential 2 When a positive point charge moves opposite the direction of an electric field π¬, the value of the electric potential V A. decreases. π¬ B. increases. C. stays the same. π π«π½ = −π¬ π πππ π½ π«π½ = positive! Q Electric Potential 3 When this point charge moves perpendicular to the direction of an electric field π¬, the value of the electric potential V A. decreases. π¬ π B. increases. C. stays the same. π = 90β Q π«π½ = −π¬ π πππ π½ π«π½ = zero! Electric Potential 4 When a negative point charge moves in the direction of an electric field π¬, the value of the electric potential V A. decreases. π¬ B. increases. C. stays the same. -Q π«π½ = −π¬ π πππ π½ π«π½ = negative Negative charge! π Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Figure 17-20, Page 754 Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Figure 17-6, Page 730 Electric Field and Electric Potential Equipotential lines indicate regions where the electrical potential is the same. Example: Positive Point Charge 1V 2V 3V 4V Equipotential lines: -Always are perpendicular to the electric field. -Spacing of lines indicate the strength of the electric field. -Electric field lines point to regions of lesser voltage. Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Figure 17-7, Page 730 Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Figure 17-8, Page 731 Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Figure 17-24, Page 755 Electric Potential 5 The figure below shows three equipotential surfaces. (The charges responsible for producing the electric potential are not shown.) Which vector shows the electric field vector at the indicated point? A π«π½ = −π¬ π πππ π½ Negative sign means electric field always points toward a decreasing V D B C Electric Potential 6 The figure below shows three equipotential surfaces. Which electric field magnitude is the largest? If the electric field magnitude is the same at any two points, state this. π«π½ = −π¬ π πππ π½ Greater change in V, greater the electric field! Capacitors Potential between two plates related to the amount of charge on the plates. q = CV Capacitance A Cο½ ο₯0 A d e0 = 8.85´10-12 m-3kg-1s4 A2 Energy in Capacitors Energy stored in a capacitor with capacitance C, Potential difference V, And stored charge q. 1 Uelectric = qV 2 1 2 Uelectric = CV 2 q Uelectric = 2C Capacitors 1 Which of the following capacitors has the largest capacitance? A. A capacitor with a potential difference of 20.0 V between its plates. The charge on the positive plate is 4.00 ο΄ 10–8 C. B. A parallel-plate capacitor with vacuum between its plates, which are separated by 0.100 mm. The area of each plate is 0.0200 m2. C. The same capacitor as in (ii) but with a dielectric with k = 1.50 filling the space between the plates. Capacitors 1 Explanation A. A capacitor with a potential difference of 20.0 V between its plates. The charge on the positive plate is 4.00 ο΄ 10–8 C. π 4 × 10−8 π=πΆπ = 2 × 10−9 F πΆ = πΆ = 20 π B. A parallel-plate capacitor with vacuum between its plates, which are separated by 0.100 mm. The area of each plate is 0.02 m2. ε0 A 8.85 × 10−12 × 0.02 −9 F πΆ = = 1.77 × 10 = d 0.1 × 10−3 C. A parallel-plate capacitor with a dielectric (πΏ = π. π) between its plates, which are separated by 0.100 mm. The area of each plate is 0.02 m2. πΆ = π πΆ0 = 1.5 × 1.77 × 10−9 F= 2.66 × 10−9 F Capacitors 2 Which of the following capacitors has the largest capacitance? A. a capacitor with potential difference 10.0 V between its plates that stores 7.50 ο΄ 10–8 J of electric potential energy B. a capacitor made up of two other capacitors, both with C = 2.00 ο΄ 10–9 F, arranged in series C. a capacitor made up of two other capacitors, both with C = 2.00 ο΄ 10–9 F, arranged in parallel Capacitors 2 Explanation A. a capacitor with potential difference 10.0 V between its plates that stores 7.50 ο΄ 10–8 J of electric potential energy −8 2π 2 × 7.5 × 10 1 −9 Uelectric = CV 2 πΆ = 2 πΆ = = 1.5 × 10 F 2 π 2 10 B. a capacitor made up of two other capacitors, both with C = 2.00 ο΄ 10–9 F, arranged in series 1/πΆ = 1/πΆ1 + 1/πΆ2 1 1 = + 2 × 10−9 2 × 10−9 πΆ = 1.00 × 10−9 F C. a capacitor made up of two other capacitors, both with C = 2.00 ο΄ 10–9 F, arranged in parallel πΆ = πΆ1 + πΆ2 = 2 × 10−9 + 2 × 10−9= 4.00 × 10−9 F Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Unnumbered Art, Page 743 Capacitors Summary Series Parallel Wiring Each capacitor on the same wire. Each capacitor on a different wire. Voltage Different for each capacitor. Vtotal ο½ V1 + V2 Same for each capacitor. Vtotal ο½ V1 ο½ V2 Charge Same for each resistor Qtotal ο½ Q1 ο½ Q2 Different for each resistor Qtotal ο½ Q1 + Q2 Decreases 1/Ceq = 1/C1 + 1/C2 Increases Ceq = C1 + C2 Capacitance Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Figure 17-11, Page 734 Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Figure 17-14, Page 741 Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Figure 17-15, Page 742 Problem Solving Find the voltage and charge across each of the 4 capacitors 20V C1 C2 C3 C4 C1 = C2 = 5F C3 = C4 = 8F Step 1: Find Equivalent Capacitance Turn all capacitors Into 1 capacitor C1 = C2 = 5F 20V C1 C2 C3 C4 C3 = C4 = 8F Ceq =? A. 6.15 F B. 10 F C. 16 F D. 26 F 20V Ceq Step 2: Find the Equivalent Charge Find the total charge (Qequiv = CequivV) Q12 = Q34 = Qequiv = 6.15 F x 20 V = 123 C C12 = 10F 20V Q12 = ? C34 = 16F Q34 = ? Step 3: Find the Voltages Work backward to find the voltage over each capacitor C12 = 10 F 20V Q12 = 123 C V12 = ? V12 = V1 = V2 = ? A. 7.7 V B. 12.3 V C. 15.4 V D. 24.6 V C34 = 16 F Q34 = 123 C V34 = ? Step 3: Find the Voltages, Cont. Work backward to find the voltage over each capacitor C12 = 10 F Q12 = 123 C 20V V12 = 12.3 V V34 = V3 = V4 = ? A. 7.7 V B. 12.3 V C. 15.4 V D. 24.6 V C34 = 16 F Q34 = 123 C V34 = ? Step 4: Find the Charges Continue working backward to find the charge on each capacitor C1 = C2 = 5F 20V C2 = 5F C1 V2 = 12.3 V Q2 = ? C3 = C4 = 8F Q1 = Q2 = ? A. 7.7 C B. 12.3 C C. 61.5 C D. 123 C C4 = 8F C3 V4 = 7.7 V Q4 = ? Answer Notice: Voltage splits in series C1 = 5F C2 = 5F V1 = 12.3 V2 = 12.3 Q1 = 61.5 C Q2 = 61.5 C C3 = 10F C4 = 10F V3 = 7.7 V4 = 7.7 Q3 = 61.5 C Q4 = 61.5 C V = V1 + V3 Q = Q3 + Q4 Notice: charge splits in parallel Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Figure 17-39, Page 757 Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Figure 17-30, Page 756 Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Figure 17-31, Page 756 Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Figure 17-10, Page 733 Electric Field Within Capacitors Electric field between two plates related to the amount of charge on the plates and the area of the plates. A q E= Ae 0 Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Figure 17-17, Page 746 Dielectric Dielectric Constant: k > 1 +Q Dielectric material -Q C ο½ k C0 E= E0 k Increases capacitance! Decreases electric field! Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Figure 17-18, Page 748 Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Unnumbered Art, Page 748 Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Figure 17-34, Page 757 Summary Electric Potential Energy: Electric Potential: Capacitance: kq1q2 Uelectric = r DUelectric = -qEdcosq kQ V= r DV = -Edcosq q = CV C ο½ k C 0 Cο½ ο₯0 A d Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Figure 17-23, Page 755 Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Figure 17-22, Page 755 Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Figure 17-35, Page 757 Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Figure 17-37, Page 757 Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Figure 17-36, Page 757 Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Figure 17-32, Page 756 Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Figure 17-38, Page 757 Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Figure 17-42, Page 758 Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Figure 17-44, Page 758 Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Figure 17-45, Page 758 Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Figure 17-33, Page 757 Material vacuum air K 1 1.00058 lipid 2.2 paraffin 2.2 paper 2.7 ceramic (porcelain) 5.8 water 80 Freedman/Ruskell/Kesten/Tauck, College Physics, 2e © 2018 W. H. Freeman and Company Table 17-1, Dielectric Constants (at 20°C and 1 atm), Page 758
