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Unformatted text preview: Chapter 19: ELECTRIC POTENTIAL ENERGY AND THE ELECTRIC POTENTIAL 1. Potential Energy 2. Potential 3. Equipotential Surfaces 4. The Millikan OilDrop Experiment 5. Capacitors 6. Capacitors in Series and in Parallel 7. Electric Field Energy 8. Dielectrics 9. Molecular Model of Induced Charge COLLEGE PHYSICS, Part II POTENTIAL ENERGY a) A tennis ball moves under the action of gravitational force. The force acting on the ball is The work done by the gravitational force is The field is conservative and the potential energy is mgh ( W = U a – U b ) b) Charge q’ in a uniform electrostatic field. The force acting on the charge is The work done by the electrostatic field is The field is conservative and the potential energy is We know that in conservative force fields, like the gravitational field, The same is true for electrostatic fields: The work doesn’t depend on the path because the force is only in the y direction, any motion in x or z directions involves zero work. Force & displacement have same direction: W > 0; U decreases Force & displacement have opp. directions: W < 0; U increases Force & displacement have same direction: W > 0; U decreases Force & displacement have opp. directions: W < 0; U increases Potential Energy of Point Charges a kqq U a ' = b kqq U b ' = and It can be shown that the work depends only on the distance from a to b and not on the details of the path. The points q , a and b do not have to be colinear. If q’ returns to a , the total work is 0. Er ' q U = 2 r q k E = For a general case, we have: and r ' qq k U = When a test charge q’ moves in the field of the source charge q from point a to point b , then U = 0 U = 0 This is valid for any combination of signs of charges. When q and q’ have the same sign, U is positive at any r , and when q and q’ have opposite signs, U is negative at any r . r r U > 0 U < 0 ∞ ∞ W = U – 0 > 0 W = U – 0 < 0 Force & displacement have same direction: W > 0 Force & displacement have opp. directions: W < 0 What is the potential energy of a charge q’ in an electrostatic field created by a number of charges? + + + = + + + = + + + = ... ' ... ' ' ' ... 3 3 2 2 1 1 3 3 2 2 1 1 3 2 1 r q r q r q kq r q q k r q q k r q q k U U U U q q q POTENTIAL The electric potential is the property of the field rather than the property of the test charge q’ ( q’ = 1). When two points have different potentials, there is a “ potential difference ”, which is often called voltage . r kqq U ' = We already know that when a charge q’ is moved from point a to point b , the work equals the difference in the potential energy at the two points: b a b a U U W = → Dividing both sides by q’ we get: b a b a b a V V q U q U q W = = → ' ' ' The potential difference between points a and b is the work done on a unit charge to transfer it from a to b ....
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This note was uploaded on 10/04/2011 for the course PHY 2054 taught by Professor Zmudskyy during the Spring '08 term at University of Central Florida.
 Spring '08
 ZMUDSKYY
 Physics, Electric Potential, Energy, Potential Energy

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