1January 25, 2005 Physics for Scientists&Engineers 2 1Physics for Scientists &Physics for Scientists &EngineersEngineers 22Spring Semester 2005Lecture 8January 25, 2005 Physics for Scientists&Engineers 2 2Electric PotentialElectric Potential We have been studying the electric field Now we will begin our study of the electric potential We showed the similarity between the gravitational forceand the electric force We demonstrated that gravitation could be described interms of a gravitational potential and we will show that theelectric potential is analogous We will show that the electric potential is can be related toenergy and work We will show that that we can calculate the electricpotential from the electric field and vice versaJanuary 25, 2005 Physics for Scientists&Engineers 2 3Electric PotentialElectric Potential EnergyEnergy The electric force, like the gravitational force, is aconservative force Thus we can define an electric potential energy, U, in termsof the work done by the electric field, We, when a systemchanges its configuration from some initial configuration tosome final configurationChange in electric potential energy = -Work done by electric field!U = Uf" Ui= "WeUi is the initial electric potential energyUf is the final electric potential energyJanuary 25, 2005 Physics for Scientists&Engineers 2 4ElectricElectric Potential Energy (2)Potential Energy (2) Like gravitational or mechanical potential energy, we mustdefine a reference point from which to define the electricpotential energy We define the electric potential energy to be zero when allcharges are infinitely far apart We can then write a simpler definition of the electricpotential taking the initial potential energy to be zero The negative sign on the work signifies that the electricforce is doing work on the charges as they are brought infrom infinity!U = Uf" 0 = U = "We2January 25, 2005 Physics for Scientists&Engineers 2 5Constant Electric FieldConstant Electric Field Let’s look at the electric potential when we move a charge qa distance d in a constant electric field The definition of work is For a constant electric field theforce is So the work done by the electric field on the charge is W =!Fi!d !F = q!E W = q!Ei!d = qEd cos!! is the angle between the electric field and the displacementJanuary 25, 2005 Physics for Scientists&Engineers 2 6Constant Electric Field - Special CasesConstant Electric Field - Special Cases Displacement is in the samedirection as the electric field• Charge loses potential energy when it moves in the direction of theelectric field Displacement is in the opposite directionfrom the electric field• Charge gains potential energy when it move in the opposite directionfrom the electric fieldW = qEd!U = "W!U = WW = !qEdJanuary 25, 2005 Physics for Scientists&Engineers 2 7Definition of the Electric PotentialDefinition of the Electric Potential The electric potential energy of a charged particle in anelectric field depends not only on the electric field but onthe charge of the particle We want to define a quantity to probe the electric fieldthat is independent of the charge of the probe We define the electric potential as Unlike the electric field, which is a vector, the electricpotential is a scalar• The electric potential has a value everywhere in space but has nodirectionV =UqJanuary 25, 2005 Physics for Scientists&Engineers 2 8Electric Potential DifferenceElectric Potential Difference The electric potential difference between aninitial point and final point f can be expressed interms of the electric potential energy at each point We can relate the change in electric potential tothe work done by the electric field on the charge!V = Vf" Vi=Ufq"Uiq=!Uq!V = "Weq3January 25, 2005 Physics for Scientists&Engineers 2 9Electric Potential Difference (2)Electric Potential Difference (2) Taking the electric potential energy to be zero atinfinity we getwhere We,∞ is the work done by the electric fieldon the charge as it is brought in from infinity The electric potential can positive, negative, orzero, but it does not have a direction The SI unit for electric potential is joules/coulombV = !We, "qJanuary 25, 2005 Physics for Scientists&Engineers 2 10The VoltThe Volt The commonly encountered unit joules/coulomb is calledthe volt, abbreviated V, after the Italian physicistAllesandro Volta (1745 - 1827) With this definition of the volt, we can express the unitsof the electric field as For the remainder of our studies, we will use the unit V/mfor the electric field1 V = 1 J1 C[E] =[F][q]=1 N1 C=1 N1 C!"#$%&1 V1 J1 C!"#$%&1 J1 N '1 m!"#$%&=1 V1 mJanuary 25, 2005 Physics for Scientists&Engineers 2 11Example - Energy Gain of a ProtonExample - Energy Gain of a Proton A proton is placed between two parallelconducting plates in a vacuum as shown.The potential difference between the twoplates is 450 V. The proton is releasedfrom rest close to the positive plate. What is the kinetic energy of the protonwhen it reaches the negative plate?The potential difference between the two plates is 450 VWe can relate the potential difference between the platesto the change in potential energy of the proton!V =!Uq+-January 25, 2005 Physics for Scientists&Engineers 2 12Example - Energy Gain of a Proton (2)Example - Energy Gain of a Proton (2)We can relate the change in potential energy to the change in kinetic energy!K = !U = q!VBecause the proton started at restK = q!VK = 1.60 "10#19 C( )450 V( )= 7.20 "10#17 J Because the acceleration of a charged particle across a potentialdifference is often used in nuclear and high energy physics, the energyunit electron-volt (eV) is common An eV is the energy gained by a charge 1 particle accelerated across anelectric potential of 1 volt The proton in this example would gain an energy of 450 eV = 0.450 keV1 eV = 1.6022 !10"19 J4January 25, 2005 Physics for Scientists&Engineers 2 13The Van de Graaff GeneratorThe Van de Graaff Generator One way to make a high electric potential is to use a Van deGraaff generator The Van de Graaff generator was invented by Robert J.Van de Graaff, an American physicist (1901 - 1967) Van de Graaff generators can produce electric potentialsup to many 10s of millions of volts Van de Graaff generators can be used to produce particleaccelerators We have been using a Van de Graaff generator in ourlecture demonstrations and we
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