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1、Electric Potential Dr.Huaqiu Deng E-mail:Electrostatic Force Is ConservativeExamples of conservative force:Features of conservative force:(1)Potential energy is associated with it(2)Work done by it is path independentElectric Potential EnergyFeatures of electric potential energy:(1)Belonged to the s
2、ystem(2)Only the difference of electric potential energy has physical meaning(3)Reference configuration of a system:charged particles are all infinitely separated from one another,corresponding reference potential energy is zeroW:the work done by the electrostatic forces between the particles during
3、 the move in from infinityProblem:Electrons are continually being knocked out of air molecules in the atmosphere by cosmic-ray（宇宇宙宙射射线线）particles coming in from space.Once released,each electron experiences an electrostatic force F due to the electric field E that is produced in the atmosphere by ch
4、arged particles already on Earth.Near Earths surface the electric field has the magnitude E=150 N/C and is directed downward.What is the change U in the electric potential energy of a released electron when the electrostatic force causes it to move vertically upward through a distance d=520 m?Sample
5、 Problem-Work and potential energy in an electric fieldSolution:Work Done by an Applied ForceEquipotential SurfaceEquipotential surface:-Formed by adjacent points that have the same potentialEqual work is done along these paths between the same surfaceNo work is done along this path on an equipotent
6、ial surface-No work is done on a charged particle by an electric field when the particle moves between points on the same equipotential surface-Can be either imaginary or realNo work is done along this path that returns to the same surface-Equal work is done on a charged particle by an electric fiel
7、d along paths between the same surfacesEquipotential SurfaceA uniform electric fieldAn electric field due to a point chargeAn electric field due to an electric dipoleFeature:equipotential surfaces are always perpendicular to electric field lines,and E is always tangent to these lines.Why?Answer:if E
8、 were not perpendicular to an equipotential surface,it would have a component lying along that surface which would do work on a charged particle as it moved along the surface,which is not true.Problem:The figure shows two points i and f in a uniform electric field E.The points lie on the same electr
9、ic field line(not shown)and are separated by a distance d.(a)Find the potential difference Vf-Vi by moving a positive test charge q0 from i to f along the path shown at Fig.(a),which is parallel to the field direction.(b)Find the potential difference Vf-Vi by moving the positive test charge q0 from
10、i to f along the path icf at Fig.(b).Sample Problem Finding the potential change from the electric fieldSolution:(a)(b)The electric field points from higher potential to lower potentialThe field is perpendicular to ic path,so there is no potential change in this pathThe field has a component along t
11、his cf path,so there is a potential change along this pathConclusion:potential is path independentPotential Due to a Point ChargeGoal:to derive an expression for the electric potential V relative to the zero potential at infinity for the space around a charged particleA positively charged particle p
12、roduces a positive electric potential.A negatively charged particle produces a negative electric potential.Problem:What is the electric potential at point P,located at the center of the square of point charges shown in the Figure?The distance d is 1.3m,and the charges are q1=+12nC,q2=-24nC,q3=+31nC,
13、q4=+17nC respectively.Sample Problem Net potential of several charged particleSolution:Cross section of Equipotential surface that contains point PPotential is different inside the squarePotential Due to an Electric DipolePotential Due to a Continuous Charge DistributionPotential Due to a Continuous
14、 Charge Distribution Charged DiskCalculating the Field from the PotentialConclusion:The component of E in any direction is the negative of the rate at which the electric potential changes with distance in that directionExample:E is uniform E is perpendicular to the equippotential surfaceProblem:The
15、electric potential at any point on the central axis of a uniformly charged disk is given bySample Problem Finding the field from the potentialSolution:Derive an expression for the electric field at any point on the axis of the disk.Electric Potential Energy of a System of Point ChargesExample:the sy
16、stem of fixed point charges Conclusion:The electric potential energy of a system of fixed point charges is equal to the work that must be done by an external agent to assemble the system,bringing each charges in from an infinite distanceProblem:Figure shows three point charges held in fixed position
17、s by forces that are not shown.What is the electric potential energy U of this system of charges?Assume that d=12cm,and that q1=+q,q2=-4q,and q3=+2q in which q=150nC.Sample Problem Potential energy of a system of three charged particlesSolution:Step 1:place q1 in place and the others are at infinity
18、Step 2:bring q2 from infinity and place it in the placeStep 3:bring q3 from infinity and place it in the place,q1 and q2 will act on q3Potential of a Charged Isolated ConductorConclusion:An excess charge placed on an isolated conductor will distribute itself on the surface of that conductor so that
19、all points of the conductor whether on the surface or inside come to the same potential.This is true if the conductor has an internal cavity and even if that cavity contains a net charge.V both inside and outside a charged spherical shell of radius 1.0m with 1.0C chargeE both inside and outside a ch
20、arged spherical shell of radius 1.0m with 1.0C chargeProblemProblem:The potential of ink-jet printer tonner core is-450V.The radius of tonner is 1cm.The resistance rate of tonner is 106/cm,and the resistance rate of ps is 1015 /cm.What are the induced potentials of tonner surface and the surface of PS?1cmPS,1015 /cm-450V106 /cm-450V-450VHomework#1 of p648#6#14#22#24#39#43#66