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Phys2212_L05 - Physics 2212 Electricity and Magnetism...

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Physics 2212 Electricity and Magnetism Lecture 5 E-fields and Charged Particles in E-Fields
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10/06/09 Physics 2212 - Lecture 5 2 E-Field of a Charged Sphere Therefore, theelectric field outsidethesurfaceof a uniformly spherically charged shell of charge Q with radius R is : sphere 2 0 1 ˆ 4 Q E r r πε = r In other words, it has thesameE-field as that produced by a point charge Q located at thecenter of the sphere. Theelectric field insidethespherical-shell is zero (becausethesum of theforces cancel). If η = Q/4 π R 2 is thesurfacechargedensity, then the surfaceE field is E surf = η / ε 0 , i.e., twiceas big as theE field of an infiniteplaneof charge. (Why?) (independent of R)
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10/06/09 Physics 2212 - Lecture 5 3 Example : A Charged Sphere A spherewith a radius R = 0.1 m has a chargeQ = 20.0 nC on its surface. What is theelectric field at a distanceof 1.0 m from thesphere? Notethat theelectric field does not depend on theradius of thesphere(becausetheE-field of a charged sphereis thesameas that of thesamechargeat a point at thecenter of the sphere.) Measuring theexternal E-field tells you thechargebut not theradius of thesphere. sphere 2 0 9 2 2 -8 2 2 1 4 (9.0 10 N m /C )(2.0 10 C)/(1.0 m) 1.8 10 N/C Q E r πε = = × × = ×
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10/06/09 Physics 2212 - Lecture 5 4 A Parallel-Plate Capacitor Theparallel platecapacitor is an important component of electronic circuits. It is constructed of two oppositely charged electrodes separated by a small gap. Thenet chargeof thecapacitor is zero. Wecan model theparallel platecapacitor as two parallel infinitecharged planes placed a distance d apart. Let thex axis go from + to -. Then wehave only to superposethefields that wehavepreviously calculated. Wefind that in thetwo regions outsidethegap thesuperposed fields cancel to give0, while in thegap they add. Therefore: outside 0 0 ˆ ˆ / 2 / 2 0 E E E i i η ε η ε + - = + = - = r r r gap 0 0 ˆ ˆ 2 / 2 / E
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