Lecture 6 Lecture 6 --Electrostatic PotentialElectrostatic PotentialChapter 28 Chapter 28 --Thursday January 25thThursday January 25th•Review of Tuesday’s class•Gauss’ law and conductors•Experimental tests of Gauss’ law•Electrostatic potential energy and vector calculus•The electrostatic potential•A tiny bit more vector calculusReading: pages 635 thru 646 (chapter 28) in HRKReading: pages 635 thru 646 (chapter 28) in HRKRead and understand the sample problemsRead and understand the sample problemsWebAssign: set 2, due tonight at 11:59pmWebAssign: set 2, due tonight at 11:59pmGraded problems (Ch. 27) Graded problems (Ch. 27) ––Ex. 15, 18, 21; Prob. 2, 10, 18Ex. 15, 18, 21; Prob. 2, 10, 18Practice problems (Ch. 28): Ex.3,15,17,27; Prob. 1,11Practice problems (Ch. 28): Ex.3,15,17,27; Prob. 1,11••Exam 1, Feb 6Exam 1, Feb 6thth, 8:30 , 8:30 ––10:10 am (10:10 am (ChsChs. 25. 25--28)28)GaussGauss’’law and conductorslaw and conductors••The electric field inside The electric field inside a conductor which is in a conductor which is in electrostatic electrostatic equilibrium must be equilibrium must be zero. zero. ••Equilibrium is reached Equilibrium is reached very quickly very quickly (<10(<10--9 9 s).s).GaussGauss’’law and conductorslaw and conductorsAn excess charge An excess charge placed on an placed on an isolated conductor isolated conductor moves entirely to moves entirely to the outer surface of the outer surface of the conductor. None the conductor. None of the excess charge of the excess charge is found within the is found within the body of the body of the conductor.conductor.GaussGauss’’law and conductorslaw and conductors••No charge resides on No charge resides on any inside surface, any inside surface, unless...unless...GaussGauss’’law and conductorslaw and conductors••No charge resides on No charge resides on any inside surface, any inside surface, unless...unless...••...a charge is placed ...a charge is placed within the cavity.within the cavity.••In this situation, In this situation, charge within the charge within the conductor moves so as conductor moves so as to screen the field set to screen the field set up by the charge in the up by the charge in the cavity. cavity. +q-------+++++++E = 0The electric field outside a conductorThe electric field outside a conductorEsurfaceouter cap inner cap sidewallsddddΦ= ⋅=⋅+⋅+⋅∫∫∫∫EAEA EA EAGGGGGGG GvvvvoEσε=The electric field outside a conductorThe electric field outside a conductor••At first sight, the At first sight, the result from the result from the previous slide previous slide seems odd in view seems odd in view of the earlier result of the earlier result for a sheet of for a sheet of charge.charge.••However, one must However, one must not forget that the not forget that the field is due not only field is due not only to the charge at the to the charge at the immediate surface, immediate surface, but also from the but also from the charge elsewhere charge elsewhere on the surface of the on the surface of the conductor.conductor.The electric field outside a conductorThe electric field outside a conductor••If the conductor is If the conductor is completely isolated completely isolated and has a uniform and has a uniform shape (e.g. sphere, shape (e.g. sphere, sheet, cylinder), sheet, cylinder), then the charge then the charge distributes evenly distributes evenly over the surface.over the surface.••If the shape is nonIf the shape is non--uniform (e.g. heart uniform (e.g. heart shape), or it is not shape), or it is not isolated, then the isolated, then the charge may be charge may be distributed highly distributed highly nonnon--uniformly.uniformly.The electric field outside a conductorThe electric field outside a conductorThe charge on a parallel plate The charge on a parallel plate capacitor resides only on the capacitor resides only on the inner surfaces. This asymmetry inner surfaces. This asymmetry occurs because neither conductor occurs because neither conductor is isolated in this situation.is isolated in this situation.••If the conductor is If the conductor is completely isolated completely isolated and has a uniform and has a uniform shape (e.g. sphere, shape (e.g. sphere, sheet, cylinder), sheet, cylinder), then the charge then the charge distributes evenly distributes evenly over the surface.over the surface.••If the shape is nonIf the shape is non--uniform (e.g. heart uniform (e.g. heart shape), or it is not shape), or it is not isolated, then the isolated, then the charge may be charge may be distributed nondistributed non--uniformly.uniformly.The electric field outside a conductorThe electric field outside a conductor++++++++++++++++++++++++++E = 0E = 0E+E+What if one plate is neutral?What if one plate is neutral?••If the conductor is If the conductor is completely isolated completely isolated and has a uniform and has a uniform shape (e.g. sphere, shape (e.g. sphere, sheet, cylinder), sheet, cylinder), then the charge then the charge distributes evenly distributes evenly over the surface.over the surface.••If the shape is nonIf the shape is non--uniform (e.g. heart uniform (e.g. heart shape), or it is not shape), or it is not isolated, then the isolated, then the charge may be charge may be distributed nondistributed non--uniformly.uniformly.The electric field outside a conductorThe electric field outside a conductorE = 0E = 0What if the neutral plate is What if the neutral plate is grounded?grounded?••If the conductor is If the conductor is completely isolated completely isolated and has a uniform and has a uniform shape (e.g. sphere, shape (e.g. sphere, sheet, cylinder), sheet, cylinder), then the charge then the charge distributes evenly distributes evenly over the surface.over the surface.••If the shape is nonIf the shape is non--uniform (e.g. heart uniform (e.g. heart shape), or it is not shape), or it is not isolated, then the isolated, then the charge may be charge may be distributed nondistributed non--uniformly.uniformly.What about less symmetric situations?What about less symmetric situations?••--QQ++++++++++++++--------------EE= 0= 021ˆ4oqrπε≠−ErGHow can we check the validity of GaussHow can we check the validity of Gauss’’and Coulomband Coulomb’’s lawss laws21ˆ4oqrδπε+=ErGSuppose:How can we check the validity of GaussHow can we check the validity
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