大二上大物新建wuelectric

1、Chap 21 Electric Potential1. Work Done by Electric Force2. Electric Potential Energy3. Electric Potential / Potential Difference 4. The Relationship between E and V(electric) potential energy(electric) potentialvolt, voltageelectron voltequipotential surfacegradientKey terms: The electric field exer

2、t electric force on a charged body placed in it. In chap 19 we define intensity of electric field to describe the property. While the electric force does work when a charged body moves in the field. So we will introduce a new physical quantity that can reflects the character of electrostatic field.2

3、1-1 Work Done by Electric Forceq0qabrFl d arbrIf q0 moves in the point charge field from a to b. the electric force on q0:r rqqEqF20004l dFdWq0qabrFl d arbrdlcosF drrqq2004barrbaabrrqqldFW200d4the work on q0 within a small displacement dl:the total work on q0 from a to b:barrqq11400 The work done by

4、 electric force does not relate to the path that the particle undergoes, it only determined by the starting and ending point.If the charged particle moves along a closed path:baabrrqqW11400011400aarrqqW00Ll dEqW,q000Ll dEIt is called the circulation flow theorem (环路定理环路定理). Electric force is a conse

5、rvative force. Electric field is a conservative field. The work done by the field is independent of the path. The work can be represented by a potential energy functionbbaarqqU,rqqU000044baUU 21-2 Electric Potential Energybabaabrrqql dEqW114000abUU U Ua and Ub are electric potential energy of q0 at

6、the electric field point a and b respectively.U,UU,W;U,UU,Wbaabbaab0 0 if0 0 ifbabal dEqUU0 then0 suppose,Ub00Uaal dEqU Potential energy is always relative to some reference point where U=0. if we choose U=0 at infinite,00Uaal dEqUaaadlcosEqldEqU 00q0qabarbraaardrqqEdrqU20004For example:rqq004 Poten

7、tial energy is a shared property of q and q0.21-3 Electric Potential.consqUa0aaaaalcosElEqlEqqUVddd000 Experiments show that at a given field point: The value is not relative to the test charge q0. It only depend on the electric field. It varies from point to point in the field, so it can reflect th

8、e properties of the field. We define it as electric potentialNotes:aaaaalcosElEqlEqqUVddd000 (1) Va can be seen as the Potential energy per unit positive charge Ua=q0Va;(2) Va can be seen as the work done by electric force on unit positive charge from point a to zero potential energy position.(3) It

9、 is a Scalar, Unit: Volt.(4) Rules for choosing zero potential point. bababaablcosElEVVVdd balElEddbaabVVV21-4 Electric Potential DifferenceaalEVdNotes:(1) Vab equals the work done by electric force on unit positive charge from a to b.(2) Vab is not relative to choose of the zero potential point.(3)

10、 In the uniform field :EdVabbababaablcosElEVVVdd 00qUqUVVVbabaab0qWab(4) baababVVqVqW0021-5 Calculations of PotentialaalEVdbabaablEVVVdababVqWVqU00，VE 1. A Point Chargedrrql dEVrPP2042. Collection of Charge ParticlesiiiiiPrqVV04r rqE204rqVP04 The potential at a given point due to any charge distribu

11、tion equals the algebraic sum of contributions from all charges present.3. Continuous Charge DistributionlsVqdddd r4dqdV0 r4dqV0aalEVdiiiiiPrqVV04Solution: VVVa,rrr2 coslrr lrrcospVa 420 Example: Find the potential of the dipole. (P.521)q q larO r r rrrrkqrqkrqk, lr POOPVVqW0Oqq0qP2lc?WOP2l2llqq0030

12、lqq003 PWSolution:Example: Electric charge Q is distributed uniformly along a line or thin rod of length l. find the potential at a point P along the perpendicular bisector or along the rod.POPYX(1) Along the rod22014llP)xx(dxV (2) Along perpendicular bisector 2l2l2202xy4dxVP 2/l4/ly2/l4/lyln422P22P

13、0 dxx2240lxlxlnPP dxdq rdxdV04 r4dqV0Example: An infinite line charge or charged conducting cylinder. Find the potential at a distance r from a very long line of charge with linear charge density .Solution:r2E0 Erabrr0barrln2EdrVVba We can not define V to be zero at infinity, because the charge dist

14、ribution itself extends to infinity. abrr0arrln2EdrVba ,0Vassumeb rrdEV1R2R ?V1222101 0 2 0RrERrRrERrE , 2112RRl dEV1202RRln Example: Electric charge is distributed uniformly around a thin ring of radius a, with total charge Q. Find the potential at a point P on the ring axis at a distance x from th

15、e center of the ring. ryOaPxxdlSolution: 220ax4dlV 220ax4Q dldq aQVo04At the center x=0 r4dqV0,ax xQV04P1R2RxOEExample: Electric charge is distributed uniformly over a circular strip of inner radius R1 and outer radius R2. The total charge is Q. Find the potential at a point P on the axis at a dista

16、nce x from the center of the strip.rdrSolution:rdr2dq 212202122024/xrrdrxrdqdV 2121212202RR/RRxrrdrdVV 22122022xRxR r4dqV0Example: A solid conducting sphere of radius R has a total charge q. Find the potential everywhere, both outside and inside the sphere. U =0.Solution: According to Gausss lawqROr

17、Rr ,rqRro,E2040 rrdEVRRrrdErdEVRrRqRq00440rrqrdEVRr04qROrROrVRRrrdErdEVRrRqRq00440What if two or more uniform charged cocentered spherical shell?rl dEV11R2RO1q2q10Rr 1Rrl dE21RRl dE2Rl dE02101114RRq20214Rqqrl dEV2 2Rrl dE2Rl dE21RrR201114Rrq20214Rqq22021212011 44 0Rr,rqqRrR,rqRro,E20210144RqRq202014

18、4Rqrqrl dEV32Rr rqq021422021212011 44 0Rr,rqqRrR,rqRro,E2020132120201212021011 44 440 44Rr,rqrqVRrR,RqrqVRr,RqRqV1R2RO1q2q12V21RR201drr4q201101R4qR4qExample: (1) An uncharged conducting sphere with radius R is placed in the field of a point charge q. The center is at a distance of l from q. Find the

19、 potential at the center O. (2) If the sphere is earthed, find the induction charge on the conductor sphereSolution:Oq lROq lRqqqOVVVV (1)l4qV0q 0 (2)qqOVVVqqVV l4qR4q00 lRqq 1. Equipotential SurfacesC)z ,y,x(V The electric potential can be represented graphically by drawing equipotential lines or,

20、in three dimensions, equipotential surfaces. An equipotential surface is one on which all points are at the same potential.21-6 The Relationship Between E and V (P.511-513)(1)The potential differences between two adjacent surfaces are equal. The place where the equipotential surfaces are dense has s

21、trong electric field. (2)The potential difference between any two points on the surface is zero, and no work is required to move a charge from one point to the other.Notes:(3)An equipotential surface must be perpendicular to the electric field at any point. The direction of the field line is the dec

22、reasing direction of the potential.(4)When all charges are at rest, the surface of a conductor is always an equipotential surface.(5)The electric field just outside a conductor must be perpendicular to the surface at every point.2. The Relation between the field and the potential To determine the di

23、fference in potential between two points if the electric field is known, we usebabaldEVV Write the equation in differential form, rVrEldEdVdldVElVdVV dlnd1P2Pn dVqdW0 EdnqndEqdW00Write the equation in differential form(P.513,dV0),ldEdVcos()EdllE dl dldVEl:Gradient of V in a particular directionIf the direction is not specified, the term gradient (梯度梯度) refers to that direction in which V changes most rapidly, this would be the direction of