PHY2061 R. D. Field Department of Physics div_3.doc Univesity of Florida Divergence of the Electric FieldConsider a sphere with radius R, volume V = 4πR3/3, and surface area A = 4πR2with a point charge Q at the center. The electric fieldfrom the charge is given by rrKQrEˆ)(2=!, and the electric fluxthrough the surface of the sphere is 02222)4()ˆˆ(επQRRKQdARKQdAnrRKQAdESSSE===⋅=⋅=Φ∫∫∫!!. The divergence of the electric fieldis given by 00000lim1lim1limρ==Φ=⋅=⋅∇→→→∫VQVAdEVEVEVSV!!!!. Volume charge density: The electric charge density is the
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This note was uploaded on 05/31/2011 for the course PHY 2061 taught by Professor Fry during the Spring '08 term at University of Florida.