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11/3/2011 Potential Energy • Gravitational Potential Energy Electric Potential Increases as you move farther from Earth Physics 122 Eyres Gravitational i U K increases U changes as you change r Uf f K U U=0 Electrical U changes as you change r = i + Ui U=0 f + K K Earth = Electrical U changes as you change r = i Udecreases - K U increases U U=0 f - K U Uf = i - Ui U=0 f - K K Udecreases U Ui Ui Uf Increases or decreases as you move farther from the charge Electrical Potential Energy-signs Electrical = mgh • Electrical Potential Energy Increases as you increase spring extension/comp ression = 12 Δ 2 = mgh Potential Energy U increases as you get farther from Earth • Spring Potential Energy + Uf + - = Exercise Is the change ∆U of the particle positive, negative, or zero as it moves from i to f? Exercise Is the change ∆U of the particle positive, negative, or zero as it moves from i to f? HINT: Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. = Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 1 11/3/2011 Electric Potential = = ! ! ! ! # − % # − % = &'() '*+ &'() '*+ ! = - ,- − ! # ,. ! % = "! # − Δ % = "# −"% ! = Δ"! A Topographic Map Checking Understanding Rank in order, from largest to smallest, the electric potentials at the numbered points. HINT: / = Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Graphical Representations of Electric Potential Δ = Δ"! −Δ0 = Δ"! Δ Can you link all three equations? = Δ"! Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 2 11/3/2011 Example Example (How is this similar to the previous problem?) 105 m/s at a point where the A proton has a speed of 3.5 x 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? A proton is released from rest at point a. It then travels past point b. What is its speed at point b? Its about Energy! How do you know? Its about Energy! How do you know? Δ Δ Δ"! Δ"! Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. The Potential Inside a Parallel-Plate Capacitor Example: (How is this similar to the previous problems?) 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). Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 123 4 Δ" Δ Slope = E Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Example Connecting Potential and Field For the situation shown in the figure, find A. The potential at points a and b.The potential difference between a and b. B. The potential energy of a proton at a and b. C. The speed at point b of a proton that was moving to the right at point a with a speed of 4.0 x 105 m/s. D. The speed at point a of a proton that was moving to the left at point b with a speed of 4.0 x 105 m/s. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 3 11/3/2011 Potential and Field for Three Important Cases Example 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? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley. 4