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...Uiuc physics em fields sources i fall semester lecture notes prof steven errede gauss law divergence theorem consider an imaginary fictitious surface enclosing surrounding e g a point charge or small charged conducting object for simplicity use sphere of radius r centered on q at origin z k nr rr er err infinitesimal area element da y x s aka gaussian is vector quantity dan dar by convention n outward pointing unit normal in this particular case because spherical symmetry problem erida flux electric field lines through measure number passing si units volt meters total tot associated with any closed the enclosed b outside will contribute nothing to since pass one portion and out another no net our calculate see above picture rri sin dd v o d polar coordinates professor department university illinois urbana champaign all rights reserved thus ddrir oo integral form if there exists lots discrete charges we know from principle superposition that gg qq iencl then...