Quiz on the math needed todayChapter 25A review of gravitational potentialIntroduction of the electric potential, a special case: the electric field is a constant.Electric Potential Energy, the general caseElectric Potential Energy, final discussionThe electric potential energy of a charge q0 in the field of a charge Q?Electric Potential, the definitionElectric Potential, the formulaPotential Difference in a Uniform FieldElectric Potential, final discussionElectric Potential, electric potential energy and WorkUnitsElectron-Volts, another unit often used in nuclear and particle physicsDirection of Electric Field, energy conservationEquipotentials = equal potentialsCharged Particle in a Uniform Field, ExamplePotential and Point ChargesPotential and Point Charges, cont.Electric Potential of a Point ChargeElectric Potential with Multiple ChargesImmediate application: Electric Potential of a DipolePotential Energy of Multiple ChargesMore About U of Multiple ChargesU with Multiple Charges, take 3 as an exampleFinding E From VFind V for an Infinite Sheet of ChargeE and V for a Point ChargeE and V for a DipoleWhen you use a computer (program) to calculate electric Potential for a Continuous Charge Distribution:V for a Continuous Charge Distribution, cont.V for a Uniformly Charged RingV for a Uniformly Charged DiskV for a Finite Line of ChargeProve that V is everywhere the same on a charged conductor in equilibriumSummarize on potential V of a charged conductor in equilibriumE Compared to VCavity in a ConductorCavity in a Conductor, contMillikan Oil-Drop Experiment – Experimental Set-UpMillikan Oil-Drop ExperimentOil-Drop Experiment, 2Oil-Drop Experiment, 3Oil-Drop Experiment, finalVan de Graaff GeneratorElectrostatic PrecipitatorQuiz on the math needed todayWhat is the result of this integral:BAdxx21)?( is what ,)()( andknown is )( If xzdxxzxyxy)?( is what ,)()( andknown is )( Ifintegral linerzsrzrr dyyBAxdxxBABA11112dxxdyxz)()( kjirrzˆˆˆyxxx system coordinateCartesian aIn ),()( Chapter 25Electric PotentialA review of gravitational potentialBWhen object of mass m is on ground level B, we define that it has zero gravitational potential energy. When we let go of this object, if will stay in place.When this object is moved to elevation A, we say that it has gravitational potential energy mgh. h is the distance from B to A. When we let go of this object, if will fall back to level B.AWhen this object is at elevation A, it has gravitational potential energy UA-UB= mgh. UA is the potential energy at point A with reference to point B. When the object falls from level A to level B, the potential energy change: ΔU =UB-UA The gravitational force does work and causes the potential energy change: W = mgh = UA-UB= -ΔU hmgWe also know that the gravitational force is conservative: the work it does to the object only depends on the two levels A and B, not the path the object moves.Introduction of the electric potential, a special case: the electric field is a constant.EF0qWhen a charge q0 is placed inside an electric field, it experiences a force from the field:When the charge is released, the field moves it from A to B, doing work:Edqq00W dEdFIf we define the electric potential energy of the charge at point A UA and B UB, then:UUUEdqBA0WIf we define UB=0, then UA= q0Ed is the electric potential energy the charge has at point A. We can also say that the electric field has an electric potential at point A. When a charge is placed there, the charge acquires an electric potential energy that is the charge times this potential.Electric Potential Energy, the general caseWhen a charge is moved from point A to point B in an electric field, the charge’s electric potential energy inside this field is changed from UA to UB:ABUUU EF0qThe force on the charge is: BABAdqWUUU sE0 force) field the(ofSo we have this final formula for electric potential energy and the work the field force does to the charge:When the motion is caused by the electric field force on the charge, the work this force does to the charge cause the change of its electric potential energy, so:UWElectric Potential Energy, final discussionElectric force is conservative. The line integral does not depend on the path from A to B; it only depends on the locations of A and B.BABAdqUUU sE0ABLine integral pathsThe electric potential energy of a charge q0 in the field of a charge Q?Qq0RReference point:We usually define the electric potential of a point charge to be zero (reference) at a point that is infinitely far away from the point charge.BABAdqUUU sE0Applying this formula:Where point A is where the charge q0 is, point B is infinitely far away. RQkdrrQkdrrQkddddˆrQkeReee222 and so ,rEsErsrEAnd the result is a scalar!So the final answer isRQqkRUe0 )( Electric Potential, the definitionThe potential energy per unit charge, U/qo, is the electric potential The potential is a characteristic of the field onlyThe potential energy is a characteristic of the charge-field systemThe potential is independent of the value of qoThe potential has a value at every point in an electric fieldThe electric potential is As in the potential energy case, electric potential also needs a reference. So it is the potential difference ΔV that matters, not the potential itself, unless a reference is specified (then it is again ΔV).oUVq=Electric Potential, the formulaThe potential is a scalar quantitySince energy is a scalarAs a charged particle moves in an electric field, it will experience a change in potentialBABAdVVV sEreference) (often thePotential Difference in a Uniform FielddEsEsEBABABAddVVVThe equations for electric potential can be simplified if the electric field is uniform:BABAVV,VVV or 0 direction, same the and i.e.,dE 0, dEWhen:This is to say that electric field lines always point in the direction of decreasing electric potentialElectric Potential, final discussionThe difference in potential is the meaningful quantityWe often take the value of the potential to be zero at some
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