Electric Potential IElectric Potential IPhysics 2102Jonathan DowlingPhysics 2102Physics 2102Lecture: 08 FRI 30 JANLecture: 08 FRI 30 JANCh24.1-5Danger!Electric Potential EnergyElectric Potential EnergyElectric Potential Energy U is Negative of the WorkW to Bring Charges in From Infinity:U!= –W∞The Change in Potential Energy ΔU Between an Initialand Final Configuration Is Negative the Work W Doneby the Electrostatic Forces:ΔU!= Uf - Ui!= -W• What is the potential energy of a singlecharge?• What is the potential energy of a dipole?• A proton moves from point i to point f in auniform electric field, as shown. - Does the electric field do positive ornegative work on the proton? - Does the electric potential energy of theproton increase or decrease?+Q–Qa+QElectric PotentialElectric PotentialElectric potential difference between two points =work per unit charge needed to move a chargebetween the two points: ΔV = Vf!–!Vi = –W/q = ΔU/q000f fi iff iidW F dsdW q E dsW dW q E dsWV V V E dsq= •= •= = •! = " = " = " •# ##!!!!!!!!Electric Potential Energy,Electric Potential Energy,Electric PotentialElectric PotentialUnits :Potential Energy = U = [J] = JoulesElectric Potential = V = U/q = [J/C] = [Nm/C] = [V] = VoltsElectric Field = E = [N/C] = [V/m] = Volts per meterElectron Volt = 1eV = Work Needed to Move an ElectronThrough a Potential Difference of 1V:W = qΔV = e x 1V = 1.60 10–19 C x 1J/C = 1.60 10–19 JEquipotential Equipotential SurfacesSurfaces• The Electric Field is Tangent to the Field Lines• Equipotential Surfaces are Perpendicular to Field Lines• Work Is Needed to Move a ChargeAlong a Field Line.• No Work Is Needed to Move a ChargeAlong an Equipotential Surface.• Electric Field Lines Always PointTowards Equipotential Surfaces WithLower Potential.0ff iiWV V V E dsq! = " = " = " •#!!Electric Field Lines and Electric Field Lines and Equipotential Equipotential SurfacesSurfaceshttp://www.cco.caltech.edu/~phys1/java/phys1/EField/EField.htmlWhy am I smiling?I’m About to Be Struck byLightning!Electric Potential and ElectricElectric Potential and ElectricPotential EnergyPotential EnergyThe change in potential energy of a charge q moving frompoint i to point f is equal to the work done by the appliedforce, which is equal to minus the work done by theelectric field, which is related to the difference inelectric potential:f i appU U U W W q V! = " = = " = !We move a proton from point i to point f ina uniform electric field, as shown.• Does the electric field do positive or negative workon the proton?• Does the electric potential energy of the protonincrease or decrease?• Does our force do positive or negative work ?• Does the proton move to a higher or lower potential?ExampleExampleConsider a positive and a negative charge, freely moving in auniform electric field. True or false?(a) Positive charge moves to points with lower potential.(b) Negative charge moves to points with lower potential.(c) Positive charge moves to a lower potential energyposition.(d) Negative charge moves to a lower potential energyposition–Q +Q0+V–V(a) True(b) False(c) True(d) True+ + + + + + + + +– – – – – – – –Conservative ForcesConservative ForcesThe potential difference between two points isindependent of the path taken to calculate it: electricforces are “conservative”.0 0ff iiW UV V V E dsq q!! = " = " = = " •#!!Summary:Summary:• Electric potential: work needed to bring +1C from infinity;units V = Volt• Electric potential uniquely defined for every point in space --independent of path!• Electric potential is a scalar — add contributions fromindividual point charges• We calculated the electric potential produced by a singlecharge: V=kq/r, and by continuous charge distributions:V=∫kdq/r• Electric potential energy: work used to build the system,charge by charge. Use W=qV for each
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