Physics 2102 Lecture 06: THU 04 FEBPowerPoint PresentationElectric Potential EnergyElectric PotentialElectric Potential Energy, Electric PotentialEquipotential SurfacesElectric Field Lines and Equipotential SurfacesElectric Potential and Electric Potential EnergyExampleConservative ForcesElectric Potential of a Point ChargeElectric Potential of Many Point ChargesSlide 13Positive WorkSlide 15Potential Energy of A System of ChargesPotential Energy of A System of Charges: SolutionSlide 18Electric Potential of a Dipole (on axis)Electric Potential on Perpendicular Bisector of DipoleSummary:Slide 22Electric Potential IElectric Potential IPhysics 2102Jonathan DowlingPhysics 2102 Physics 2102 Lecture 06: THU 04 FEBLecture 06: THU 04 FEBDanger!QuickTime™ and a decompressorare needed to see this picture.4π3R34πR2πR22πRπR2L2πRLVolume [m3]Area [m2]Circumference [m]L ×L ×ddRddRLRRRSphereCircleCylinderElectric Potential EnergyElectric Potential EnergyElectric Potential Energy U is Negative of the Work W to Bring Charges in From Infinity: U= –W∞The Change in Potential Energy U Between an Initial and Final Configuration Is Negative the Work W Done by the Electrostatic Forces:U= Uf - Ui= -W• What is the potential energy of a single charge? • What is the potential energy of a dipole? • A proton moves from point i to point f in a uniform electric field, as shown. - Does the electric field do positive or negative work on the proton? - Does the electric potential energy of the proton increase or decrease? +Q–Qa+QElectric PotentialElectric PotentialElectric potential difference between two points = work per unit charge needed to move a charge between the two points: V = Vf–Vi = –W/q = U/q000f fi iff iidW F dsdW q E dsW dW q E dsWV V V E dsq= •= •= = •Δ = − =− =− •∫ ∫∫rrrrrrrrElectric Potential Energy, Electric Potential Energy, Electric PotentialElectric PotentialUnits : Potential Energy = U = [J] = Joules Electric 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 Electron Through a Potential Difference of 1V:W = qV = e x 1V = 1.60 10–19 C x 1J/C = 1.60 10–19 JEquipotential SurfacesEquipotential Surfaces• The Electric Field is Tangent to the Field Lines• Equipotential Surfaces are Perpendicular to Field Lines• Work Is Needed to Move a Charge Along a Field Line.• No Work Is Needed to Move a Charge Along an Equipotential Surface. • Electric Field Lines Always Point Towards Equipotential Surfaces With Lower Potential. 0ff iiWV V V E dsqΔ = − =− =− •∫rrElectric Field Lines and Equipotential Electric Field Lines and 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 Electric Electric Potential and Electric Potential EnergyPotential EnergyThe change in potential energy of a charge q moving from point i to point f is equal to the work done by the applied force, which is equal to minus the work done by the electric field, which is related to the difference in electric potential:f i appU U U W W q VΔ = − = =− = ΔWe move a proton from point i to point f in a uniform electric field, as shown. • Does the electric field do positive or negative work on the proton? • Does the electric potential energy of the proton increase 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 a uniform 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 energy.(d) Negative charge moves to a lower potential energy.–Q +Q 0+V–V(a) True(b) False(c) True(d) True+ + + + + + + + +– – – – – – – –Conservative ForcesConservative ForcesThe potential difference between two points is independent of the path taken to calculate it: electric forces are “conservative”. 0 0ff iiW UV V V E dsq qΔΔ = − =− = =− •∫rrElectric Potential of a Point Electric Potential of a Point ChargeCharge2fPiRRV E ds E dskQ kQ kQdrr r R∞∞∞=− ⋅ =− ==− =+ =+∫ ∫∫rrNote: if Q were anegative charge,V would be negativeElectric Potential of Many Point Electric Potential of Many Point ChargesCharges•Electric potential is a SCALAR not a vector.•Just calculate the potential due to each individual point charge, and add together! (Make sure you get the SIGNS correct!)q1q5q4q3q2∑=iiirqkVr1r2r3r4r5PElectric Potential and Electric Potential and Electric Potential EnergyElectric Potential EnergyappU W q VΔ = = ΔappU W q VΔ = = Δ+Q–QaWhat is the potential energy of a dipole?+Q• First: Bring charge +Q: no work involved, no potential energy.• The charge +Q has created an electric potential everywhere, V(r)= kQ/r –Qa• Second: The work needed to bring the charge –Q to a distance a from the charge +Q is Wapp=U = (-Q)V = (–Q)(+kQ/a) = -kQ2/a• The dipole has a negative potential energy equal to -kQ2/a: we had to do negative work to build the dipole (electric field did positive work).Positive Positive WorkWorkNegative Negative WorkWork+Q+Qa+Q–QaPositive Positive WorkWorkNegative Negative WorkWork+Q+Qa+Q–QaCharge Moves DownhillQuickTime™ and a decompressorare needed to see this picture.Charge Moves UphillPotential Energy of A System of Potential Energy of A System of ChargesCharges•4 point charges (each +Q and equal mass) are connected by strings, forming a square of side L•If all four strings suddenly snap, what is the kinetic energy of each charge when they are very far apart?•Use conservation of energy:–Final kinetic energy of all four charges = initial potential energy stored = energy required to assemble the system of charges+Q+Q+Q+QLet’s do this from scratch! QuickTime™ and a decompressorare needed to see this picture.Potential Energy of A System Potential Energy of A System of Charges: Solutionof Charges: Solution•No energy needed to bring in first charge: U1=022 1kQU QVL= =•Energy needed to bring in 2nd charge:2 23 1 2( )2kQ kQU QV Q V VLL= = + = +•Energy needed to bring in 3rd charge =•Energy needed to bring in 4th charge =+Q+Q+Q+QTotal potential energy is sum of all
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