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ism_chapter_22 - Chapter 22 The Electric Field 2 Continuous...

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79 Chapter 22 The Electric Field 2: Continuous Charge Distributions Conceptual Problems *1 •• ( a ) False. Gauss’s law states that the net flux through any surface is given by inside S n net 4 kQ dA E π φ = = . While it is true that Gauss’s law is easiest to apply to symmetric charge distributions, it holds for any surface. ( b ) True 2 •• Determine the Concept Gauss’s law states that the net flux through any surface is given by inside S n net 4 kQ dA E π φ = = . To use Gauss’s law the system must display some symmetry. 3 ••• Determine the Concept The electric field is that due to all the charges, inside and outside the surface. Gauss’s law states that the net flux through any surface is given by inside S n net 4 kQ dA E π φ = = . The lines of flux through a Gaussian surface begin on charges on one side of the surface and terminate on charges on the other side of the surface. 4 •• Picture the Problem We can show that the charge inside a sphere of radius r is proportional to r 3 and that the area of a sphere is proportional to r 2 . Using Gauss’s law, we can show that the field must be proportional to r 3 / r 2 = r . Use Gauss’s law to express the electric field inside a spherical charge distribution of constant volume charge density: A kQ E inside 4 π = where 2 4 r A π = . Express Q inside as a function of ρ and r : 3 3 4 inside r V Q πρ ρ = = Substitute to obtain: r k r r k E 3 4 4 4 2 3 3 4 πρ π πρ π = =

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