Lecture 7 Lecture 7 --Electrostatic PotentialElectrostatic PotentialChapter 28 Chapter 28 --Tuesday January 30thTuesday January 30th•Review of electrostatic potential energy•The electrostatic potential •Many example problems•Equipotential surfacesReading: pages 635 thru 652 (chapter 28) in HRKReading: pages 635 thru 652 (chapter 28) in HRKRead and understand the sample problemsRead and understand the sample problemsWebAssignWebAssignhomework: set 3, due Sun. 4th at 11:59pmhomework: set 3, due Sun. 4th at 11:59pmGraded problems (Ch. 28) Graded problems (Ch. 28) ––Ex. 2, 12, 16, 24; Prob. 6, 13Ex. 2, 12, 16, 24; Prob. 6, 13Practice problems (Ch. 28):Practice problems (Ch. 28):Ex. 29, 31, 43, 47; Prob. 15Ex. 29, 31, 43, 47; Prob. 15••Exam 1, Feb 6Exam 1, Feb 6thth, 8:30 , 8:30 ––10:10 am (10:10 am (ChsChs. 25. 25--28)28)••Review sessions: Thurs. 5:30 pm and Mon. 5:00 pmReview sessions: Thurs. 5:30 pm and Mon. 5:00 pmElectrostatic Potential EnergyElectrostatic Potential EnergyConsider the analogy with gravitation:Consider the analogy with gravitation:12122214EGoqqmmFFGrrπε==In the gravitational case, we defined differences In the gravitational case, we defined differences in potential energy in the following way:in potential energy in the following way:1211ffi ififiUU U W d Gmmrr⎛⎞Δ= − =− =− ⋅ =− −⎜⎟⎜⎟⎝⎠∫FsGGYou were, no doubt, told that gravity is a You were, no doubt, told that gravity is a conservative force. Thus, the above result does conservative force. Thus, the above result does not depend on the path taken between not depend on the path taken between rriiand rand rff..12 1 212 122212 121ˆˆ4EGoqq mmGrrπε−==FrFrGGElectrostatic Potential EnergyElectrostatic Potential Energy••Thus, it should not surprise you that the electrostatic Thus, it should not surprise you that the electrostatic force is conservative also.force is conservative also.••It is this property that allows us to define a scalar It is this property that allows us to define a scalar potential energy potential energy ((one cannot do this for non one cannot do this for non conservative forcesconservative forces))..121114baobaUd qqrrπε⎛⎞Δ=− ⋅ = −⎜⎟⎠+⎝∫FsGGElectrostatic Potential EnergyElectrostatic Potential Energy••Thus, it should not surprise you that the electrostatic Thus, it should not surprise you that the electrostatic force is conservative also.force is conservative also.••It is this property that allows us to define a scalar It is this property that allows us to define a scalar potential energy potential energy ((one cannot do this for non one cannot do this for non conservative forcesconservative forces))..Path independencePath independencebaUdΔ=− ⋅∫FsGGElectrostatic Potential EnergyElectrostatic Potential Energy••Just like the gravitational force, it should not surprise Just like the gravitational force, it should not surprise you that the electrostatic force is conservative also.you that the electrostatic force is conservative also.••It is this property that allows us to define a scalar It is this property that allows us to define a scalar potential energy potential energy ((one cannot do this for non one cannot do this for non conservative forcesconservative forces))..121114baobaUd qqrrπε⎛⎞Δ=− ⋅ = −⎜⎟⎠+⎝∫FsGGThe sign of The sign of ΔΔUUis not a problem. It is taken is not a problem. It is taken care of by the signs of the charges care of by the signs of the charges qq11andandqq22..⊕⊕⊕⊕−−−−−⊕−ΔΔUUWWEEWWextext++−−++−−++−−−−++−−++−−++−−++−−++−−++⊕Electrostatic Potential EnergyElectrostatic Potential EnergyElectrostatic Potential EnergyElectrostatic Potential Energy••The potential energy is a property of both of the The potential energy is a property of both of the charges, not one or the other.charges, not one or the other.••If we choose a reference such that U = If we choose a reference such that U = 00when the when the charges are infinitely far apart, then we can simplify charges are infinitely far apart, then we can simplify the expression for the potential energy as follows.the expression for the potential energy as follows.12121111()44rooqqUr d qqrrπε πε∞⎛⎞=− ⋅ = − =⎜⎟∞⎝⎠+∫FsGGAgain, the sign of Again, the sign of UUis not a problem. It is is not a problem. It is taken care of by the signs of the charges taken care of by the signs of the charges qq11andandqq22..Potential Energy of a System of ChargesPotential Energy of a System of Chargesq10U =q2r12121214oqqUrπε=q3r1312 1312 131144ooqq qqUrrπε πε=+r2312 13 2312 13 23111444oooqq qq qqUrrrπε πε πε=++Assumes that the Assumes that the superposition superposition principle is validprinciple is validThe Electrostatic PotentialThe Electrostatic Potential••Suppose we take a test charge qSuppose we take a test charge q00and move it from and move it from point a to point b under the influence of the force due point a to point b under the influence of the force due to a system of source charges to a system of source charges qqii. The potential energy . The potential energy depends on the magnitude of the test charge.depends on the magnitude of the test charge.••We can eliminate the test charge from the problem in We can eliminate the test charge from the problem in exactly the same fashion as we did in chapter 26 when exactly the same fashion as we did in chapter 26 when defining the electric field. In doing so, we define a new defining the electric field. In doing so, we define a new quantity known as the Electrostatic Potential quantity known as the Electrostatic Potential difference difference ΔΔV:V:babaoo oUUU WVVVqq qΔ−Δ= − = = =−••This This ‘‘scalar potentialscalar potential’’depends only on the details of depends only on the details of the static charge distribution.the static charge distribution.The Electrostatic PotentialThe Electrostatic Potential••We can eliminate the test charge from the problem in We can eliminate the test charge from the problem in exactly the same fashion as we did in chapter 26 when exactly the same fashion as we did in chapter 26 when defining the electric field. In doing so, we define a new defining the electric field. In doing so, we define a new quantity known as the Electrostatic Potential quantity known as the Electrostatic Potential
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