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Phys2212_29.5+to+29.7 - Physics 2212 Electricity and...

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Physics 2212 Electricity and Magnetism Lecture 11 (Knight: 29.5 to 29.7) Electric Potential, Equipotential Surfaces and E = - r V
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10/06/09 Physics 2212 - Lecture 11 2 The Electric Potential In Chapter 25 weintroduced theconcept of an electric field E , which can be though of as a normalized force, i.e., E = F/ q , thefield E that would producea force F on sometest charge q . Wecan similarly definethe electric potential V as a charge-normalized potential energy, i.e., V=U elec /q , theelectric potential V that would givea test charge q an electric potential energy U elec becauseit is in thefield of someother sourcecharges. Wedefinethe unit of electric potential as the volt : 1 volt = 1 V = 1 J/C = 1 Nm/C. Other units are: kV=10 3 V, mV=10 -3 V, and V=10 -6 V. Example: A D-cell battery has a potential of 1.5 V between its terminals.
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10/06/09 Physics 2212 - Lecture 11 3 What Good is the Electric Potential? Liketheelectric field E , theelectric potential V is an abstract idea. It offers an advantage, however, becauseit is a scalar quantity while E is a vector, yet thetwo can beconverted to each other. It is useful because: l Theelectric potential V depends only on thecharges and their geometries. Theelectric potential is the “ability” of thesourcecharges to havean interaction if a charge q shows up. Thepotential is present in all space, whether or not a chargeis thereto experienceit. l If weknow theelectric potential V throughout a region of space, we’ll immediately know the potential energy U = qV of any charge q that enters that region. Losing Potential Energy Gaining Kinetic Energy Gaining Potential Energy Losing Kinetic Energy
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10/06/09 Physics 2212 - Lecture 11 4 Example : Moving Through a Potential Difference A proton with a speed of v i = 2.0 x 10 5 m/s enters a region of spacewheresourcecharges havecreated an electric potential. What is theproton’s speed after it has moved through a potential differenceof V = 100 V? f f i i K qV K qV + = + f i i f i K K qV qV K q V = + - = - 1 1 2 2 2 2 f i mv mv q V = - 2 5 2 1.44 10 m/s f i e v v V m = - = × What is v f if theproton is replaced by an electron? 2 6 2 (electron) 5.93 10 m/s f i e e v v V m = + = ×
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10/06/09 Physics 2212 - Lecture 11 5 The Electric Potential Inside a Parallel Plate Capacitor -9 2 3.0 mm, =4.42 10 C/m d η = × ( 29 0 , to - 500 N/C, to right E η ε = + = elec q+sources
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