Lightning Review15.10 Electric Flux and Gauss’s Law15.10 Electric Flux15.10 Electric Flux15.10 Electric Flux15.10 Electric FluxExample:15.10 Gauss’s Law15.10 Gauss’s Law16.0 Introduction16.1 Potential difference and electric potentialPotential energy of electrostatic fieldElectric potentialElectric potential - unitsElectric potential - notesAnalogy between electric and gravitational fieldsExample: motion of an electron16.2 Electric potential and potential energy due to point chargesSuperposition principle for potentialsPotential energy of a system of point chargesMini-quiz: potential energy of an ion16.3 Potentials and charged conductorsThe electron voltProblem-solving strategyExample : ionization energy of the electron in a hydrogen atom16.4 Equipotential surfaces119/9/20039/9/2003General Physics (PHY 2140)Lecture 4Lecture 4¾ Electrostatics9 Electric flux and Gauss’s law9 Electrical energy9 potential difference and electric potential9 potential energy of charged conductorsChapters 15-16http://www.physics.wayne.edu/~apetrov/PHY2140/229/9/20039/9/2003Lightning ReviewLightning ReviewLast lecture:1. Properties of the electric field, field lines2. Conductors in electrostatic equilibrium99Electric field is zero everywhere within the conductor.Electric field is zero everywhere within the conductor.99Any excess charge field on an isolated conductor resides on its Any excess charge field on an isolated conductor resides on its surface.surface.99The electric field just outside a charged conductor is perpendicThe electric field just outside a charged conductor is perpendicular to the ular to the conductor’s surface.conductor’s surface.99On an irregular shaped conductor, the charge tends to accumulateOn an irregular shaped conductor, the charge tends to accumulateat at locations where the radius of curvature of the surface is smallelocations where the radius of curvature of the surface is smallest.st.Review Problem: Would life be different if the electron were positively charged and the proton were negatively charged? Does the choice of signs have any bearing on physical and chemical interactions?339/9/20039/9/200315.10 Electric Flux and Gauss’s Law15.10 Electric Flux and Gauss’s LawA convenient technique was introduced by Karl F. Gauss A convenient technique was introduced by Karl F. Gauss (1777(1777--1855) to calculate electric fields.1855) to calculate electric fields.Requires symmetric charge distributions.Requires symmetric charge distributions.Technique based on the notion of Technique based on the notion of electrical fluxelectrical flux..449/9/20039/9/200315.10 Electric Flux15.10 Electric FluxTo introduce the notion of flux, consider To introduce the notion of flux, consider a situation where the electric field is a situation where the electric field is uniform in magnitude and direction. uniform in magnitude and direction. Consider also that the field lines cross a Consider also that the field lines cross a surface of area A which is surface of area A which is perpendicular to the field.perpendicular to the field.The number of field lines per unit of The number of field lines per unit of area is constant.area is constant.The flux, The flux, ΦΦ, is defined as the product of , is defined as the product of the field magnitude by the area crossed the field magnitude by the area crossed by the field lines.Area=AEby the field lines.EAΦ=559/9/20039/9/200315.10 Electric Flux15.10 Electric FluxUnits: NmUnits: Nm22/C in SI units./C in SI units.Find the electric flux through the area A = 2 mFind the electric flux through the area A = 2 m22, which is , which is perpendicular to an electric field E=22 N/Cperpendicular to an electric field E=22 N/CEAΦ=Answer: Answer: ΦΦ= 44 Nm2/C.= 44 Nm2/C.669/9/20039/9/200315.10 Electric Flux15.10 Electric FluxIf the surface is not perpendicular to the field, the If the surface is not perpendicular to the field, the expression of the field becomes:expression of the field becomes:Where Where θθis the angle between the field and a normal to is the angle between the field and a normal to the surface.the surface.cosEAθΦ=θθNθθ779/9/20039/9/200315.10 Electric Flux15.10 Electric FluxRemark: Remark: When an area is constructed such that a closed surface When an area is constructed such that a closed surface is formed, we shall adopt the convention that the flux is formed, we shall adopt the convention that the flux lines passing lines passing intointothe interior of the volume are the interior of the volume are negativenegativeand those passing and those passing out ofout ofthe interior of the volume are the interior of the volume are positivepositive..889/9/20039/9/2003Example:Example:Question:Question:Calculate the flux of a constant E field (along x) through a Calculate the flux of a constant E field (along x) through a cube of side “L”.cube of side “L”.xyzE12999/9/20039/9/2003Question:Question:Calculate the flux of a constant E field (along x) through a cubCalculate the flux of a constant E field (along x) through a cube of side “L”.e of side “L”.Reasoning:Reasoning:zzDealing with a composite, closed surface.Dealing with a composite, closed surface.zzSum of the fluxes through all surfaces.Sum of the fluxes through all surfaces.zzFlux of field going in is negativeFlux of field going in is negativezzFlux of field going out is positive.Flux of field going out is positive.zzE is parallel to all surfaces except surfaces labeled 1 and 2.E is parallel to all surfaces except surfaces labeled 1 and 2.zzSo only those surface contribute to the flux.So only those surface contribute to the flux.Solution:Solution:xyzE12220netEL ELΦ=− + =2111cosEAELθΦ=− =−2222cosEAELθΦ= =10109/9/20039/9/200315.10 Gauss’s Law15.10 Gauss’s LawThe net flux passing through a closed surface The net flux passing through a closed surface surrounding a charge Q is proportional to the magnitude surrounding a charge Q is proportional to the magnitude of Q:of Q:In free space, the constant of proportionality is 1/In free space, the constant of proportionality is 1/εεoowhere where εεoois called the permittivity of of free space.cosnetEAQθΦ= ∝∑is called the permittivity of of free space.()12 2 2922118.85 10448.9910 /oeCNmkNm Cεππ−== =× ⋅×11119/9/20039/9/200315.10 Gauss’s Law15.10 Gauss’s LawThe net flux passing through any closed surface is equal The net flux passing through any closed surface is equal to the net charge