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# div_3 - PHY2061 R D Field Divergence of the Electric Field...

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PHY2061 R. D. Field Department of Physics div_3.doc Univesity of Florida Divergence of the Electric Field Consider a sphere with radius R, volume V = 4 π R 3 /3, and surface area A = 4 π R 2 with a point charge Q at the center. The electric field from the charge is given by r r KQ r E ˆ ) ( 2 = ! , and the electric flux through the surface of the sphere is 0 2 2 2 2 ) 4 ( ) ˆ ˆ ( ε π Q R R KQ dA R KQ dA n r R KQ A d E S S S E = = = = = Φ ! ! . The divergence of the electric field is given by 0 0 0 0 0 lim 1 lim 1 lim ε ρ ε = = Φ = = V Q V A d E V E V E V S V ! ! ! ! . Volume charge density: The electric charge density is the
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