Lecture 41: FRI 01 MAYLecture 41: FRI 01 MAYFinal Exam ReviewFinal Exam ReviewPhysics 2102Jonathan DowlingA few concepts:A few concepts:electric force, field and potentialelectric force, field and potential• Electric force:– What is the force on a charge produced by othercharges?– What is the force on a charge when immersed in anelectric field?• Electric field:– What is the electric field produced by a system ofcharges? (Several point charges, or a continuousdistribution)• Electric potential:– What is the potential produced by a system ofcharges? (Several point charges, or a continuousdistribution)Plus a few other itemsPlus a few other items……• Electric field lines, equipotential surfaces: lines go from +ve to–ve charges; lines are perpendicular to equipotentials; lines(and equipotentials) never cross each other…• Gauss’ law: Φ=q/ε0 . Given the field, what is the chargeenclosed? Given the charges, what is the flux? Use it todeduce formulas for electric field.• Electric dipoles: field and potential produced BY a dipole,torque ON a dipole by an electric field, potential energy of adipole• Electric potential, work and potential energy: work to bring acharge somewhere is W = –qV (signs!). Potential energy of asystem = negative work done to build it.• Conductors: field and potential inside conductors, and on thesurface.• Shell theorem: systems with spherical symmetry can bethought of as a single point charge (but how much charge?)• Symmetry, and “infinite” systems.Conductors and insulatorsConductors and insulators• Will two charged objects attractor repel?• Can a charged object attract orrepel an uncharged object?• What is the electric field inside aconductor?• What is the direction of theelectric field on the surface of aconductor?• What happens to a conductorwhen it is immersed in an electricfield?Electric forces and fields: point chargesElectric forces and fields: point chargesFigure 22N-14 shows an arrangement of four charged particles, with angle θ = 34°and distance d = 2.20 cm. The two negatively charged particles on the y axis areelectrons that are fixed in place; the particle at the right has a charge q2 = +5e(a) Find distance D such that the net force on theparticle at the left, due to the three other particles,is zero.(b) If the two electrons were moved further from thex axis, would the required value of D be greaterthan, less than, or the same as in part (a)?Other possible questions: what’s the electric field produced by the chargesXXX at point PPP ? what’s the electric potential produced by the charges XXXat point PPP ? What’s the potential energy of this system?Electric dipolesElectric dipoles• What’s the electric field atthe center of the dipole?On axis? On the bisector?far away?• What is the force on adipole in a uniform field?• What is the torque on adipole in a uniform field?• What is the potentialenergy of a dipole in auniform field?Electric fields of distributed chargesElectric fields of distributed chargesPossible problems, questions:• What’s the electric field at the centerof a charged circle?• What’s the electric field at the centerof ¼ of a charged circle?• What’s the electric field far from thering? far from the disk?• What’s the electric field of aninfinite disk?GaussGauss’’ law lawA long, non conducting, solid cylinder of radius 4.1 cm has a nonuniform volumecharge density that is a function of the radial distance r from the axis of thecylinder, as given by ρ = Ar2, with A = 2.3 µC/m5.(a) What is the magnitude of the electric field at a radial distance of 3.1 cm fromthe axis of the cylinder?(b) What is the magnitude of the electric field at a radial distance of 5.1 cm fromthe axis of the cylinder?At each point on the surface of the cube shown in Fig. 24-26, the electric field is inthe z direction. The length of each edge of the cube is 2.3 m. On the top surface ofthe cube E = -38 k N/C, and on the bottom face of the cube E = +11 k N/C.Determine the net charge contained within the cube.[-2.29e-09] CGaussGauss’’ law lawGaussGauss’’ law: applications law: applicationsElectric potential, electric potentialElectric potential, electric potentialenergy, workenergy, workIn Fig. 25-39, point P is at the center of the rectangle. With V = 0 at infinity, what isthe net electric potential in terms of q/d at P due to the six charged particles?The figure shows conducting plates with area A=1m2, andthe potential on each plate. Assume you are far from theedges of the plates.• What is the electric field between the plates in each case?• What (and where) is the charge density on the plates incase (1)?• What happens to an electron released midway betweenthe plates in case (1)?Derive an expression in terms of q2/a for the work required to set up the four-charge configuration of Fig. 25-50, assuming the charges are initially infinitely farapart.The electric potential at points in an xy plane is given by V = (2.0 V/m2)x2 - (4.0V/m2)y2. What are the magnitude and direction of the electric field at point (3.0m, 3.0 m)?• Questions: from checkpoints andquestions in the textbook!U = −5U0, −7U0, +3U0, +5U0ProblemProblem• Calculate electric field at point P.PxLadxE• Field very far away?Potential of Continuous Charge DistributionPotential of Continuous Charge Distribution/Q L!=dxdq!=!!"+==LxaLdxkrkdqV0)(#[ ]LxaLk0)ln( !+!="!"#$%&+=aaLkV ln'• Uniformly charged rod• Total charge Q• Length L• What is V at position Pshown?PxLadxProblemProblemField at center of arc?Line Of Charge: Field on bisectorLine Of Charge: Field on bisector Distance22xad +=2)(ddqkdE =Lq=!Charge per unit length2/322)()(cosxaadxkdEdEy+==!"QLaPoxdE!dxd2/122)(cosxaa+=!Line Of Charge: Field on bisectorLine Of Charge: Field on bisector!"+=2/2/2/322)(LLyxadxakE#What is E very far away from the line (L<<a)?2242LaaLk+=!2/2/222LLaxaxak!"#$%&'+=(akLaLkEy!!222==Ey~2kλL/a(2a)=kλL/a2=kq/a2What is E if the line is infinitely long (L >> a)?Problem: GaussProblem: Gauss’’ Law to Find E Law to Find EGaussGauss’’ Law: Cylindrical Symmetry Law: Cylindrical SymmetryRLEAE!2|||| =="00!"!Lq==#RkRRLLE!"#!"#!222||00===• Approximate as infinitely longline — E radiates outwards.• Choose cylindrical surface ofradius R, length L co-axial withline of charge.R = 1 mmE = ?1 mPotential Energy of aPotential Energy of aSystem of ChargesSystem of ChargesPotential Energy of A System of ChargesPotential
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