# L08 - Lecture 8 Electrostatic Field and Potential Gradient...

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LECTURE 8 slide 1 Lecture 8 Electrostatic Field and Potential Gradient Sections: 4.5, 4.6 Homework: D4.6, D4.7, D4.8; 4.16, 4.17, 4.18, 4.19, 4.20, 4.22, 4.23, 4.24, 4.25

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LECTURE 8 slide 2 Conservative Property of Potential of Point Charge – 1 the potential of a single point charge at the origin depends solely on the radial distance to the observation point A (see L07) 1 4 A A Q V r πε = the potential difference V AB between points A and B depends solely on the their radial distances from the origin N 2 11 4 4 B A r B AB r r A B Ar d QQ Vd d r rr r ⎛⎞ =⋅= = ⎜⎟ ⎝⎠ ∫∫ L EL aa angular positions, θ and φ , of observation points do not matter + A A r E B B r path of integration does not matter – integrand has only r component and r dependence
LECTURE 8 slide 3 Conservative Property of Potential of Point Charge – 2 11 0 4 AB AA c Q Vd rr πε ⎛⎞ = ⋅= = ⎜⎟ ⎝⎠ EL v if path of integration is closed – potential difference is zero + A B A r E c vector field whose closed-path integral is zero for any closed contour is called conservative

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LECTURE 8 slide 4 Superposition of Potential potential of discrete (point) charges 0 1 1 () 4 || N n n n Q V πε = = r rr this is an algebraic superposition potential due to distributed charge 0 1( ) , V 4| | v P v VV d v ρ == ∫∫∫ r r 0 ) , V | s s Vd s = ∫∫ r r 0 ) , V 4|| l L l = r r x y z r P r Q v
LECTURE 8 slide 5 Conservative Property of Electrostatic Potential conservative property of potential follows from superposition and conservative property of potential of point charge

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## This note was uploaded on 02/29/2012 for the course PHYS 227 taught by Professor Rabe during the Fall '08 term at Rutgers.

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L08 - Lecture 8 Electrostatic Field and Potential Gradient...

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