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Chapter 21 Electric Potential Topics: • Electric potential energy • Electric potential • Conservation of energy • Capacitors and Capacitance 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? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Analyzing a square of charges Energy to Assemble Wme = PEE = PEEf - PEEi (PEEi = 0 J) PEEf = q1Vnc@1 + q2V1@2 + q3V12@3 + q4V123@4 V123@4 = V1@4 +V2@4 + V3@4 Energy to move (Move 2q from Corner to Center) Wme = PEE = PEEf - PEEi = q2qV123@center - q2qV123@corner Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Example Problem Source charges create the electric potential shown. A. What is the potential at point A? At which point, A, B, or C, does the electric field have its largest magnitude? B. Is the magnitude of the electric field at A greater than, equal to, or less than at point D? C. What is the approximate magnitude of the electric field at point C? D. What is the approximate direction of the electric field at point C? Slide 21-33 Example Problem A proton is released from rest at point a. It then travels past point b. What is its speed at point b? Slide 21-23 Example Problem A parallel-plate capacitor is held at a potential difference of 250 V. A proton is fired toward a small hole in the negative plate with a speed of 3.0 x 105 m/s. What is its speed when it emerges through the hole in the positive plate? (Hint: The electric potential outside of a parallel-plate capacitor is zero). Slide 21-26 Example Problem What is Q2? Slide 21-35 Electric Potential Energy Example Problem The electric field between two charged plates is uniform with a strength of 4 N/C. a. Draw several electric field lines in the region between the plates. b. Determine the change in electrical potential energy in moving a positive 4 microCoulomb charge from A to B. c. Determine the change in electrical potential energy in moving a negative 12 microCoulomb charge from A to B. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Gravitational Potential Energy: Example Problem 2 A spacecraft is launched away from earth a. Draw several gravitational field lines in the region around Earth. b. Determine the change in gravitational potential energy when the spacecraft moves from A to B, where A is 10 million miles from Earth and B is 30 million miles from Earth. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Electric Potential Energy: Example Problem 3 A small charge moves farther from a positive source charge. a. Draw several electric field lines in the region around the source charge. b. Determine the change in electrical potential energy in moving a positive 4 nC charge from A to B, where A is 3 cm from the source charge and B is 10 cm away. c. Determine the change in electrical potential energy in moving a negative 4 nC charge from A to B. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Electric Potential Energy & Electric Potential: Example Problem 4 A proton has a speed of 3.5 x 105 m/s at a point where the electrical potential is 600 V. It moves through a point where the electric potential is 1000 V. What is its speed at this second point? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Define Capacitance Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 The Capacitance of a Parallel-Plate Capacitor C= e0 A d Slide 21-31 Capacitance and Capacitors The charge ±Q on each electrode is proportional to the potential difference ΔVC between the electrodes: Q = CDVC Slide 21-29 Discuss Batteries Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 Batteries The potential difference between the terminals of a battery, often called the terminal voltage, is the battery’s emf. W chem ∆Vbat = ____ = q Slide 22-12 Charging a Capacitor Slide 21-30 Dielectrics and Capacitors Slide 21-32 Dielectric Constant With a dielectric between its plates, the capacitance of a parallel-plate capacitor is increased by a factor of the dielectric constant κ: C= ke 0 A d Slide 21-33 Energy stored in Capacitor – Storing Energy in E-field Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Slide 21-16 A Conductor in Electrostatic Equilibrium Slide 21-27