hw1 - 1 Phys6103 Homework set#1 1 Gauss’ Law Practice Use...

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Unformatted text preview: 1 Phys6103: Homework set #1 1 Gauss’ Law Practice Use Gauss’ law to find the electric field when the charge density is (a) ρ ( x ) = ρ exp n- κ √ x 2 o . Express the answer in Cartesian coordinates. (b) ρ ( x,y ) = ρ exp n- κ p x 2 + y 2 o . Express the answer in cylindrical coordinates. (c) ρ ( x,y,z ) = ρ exp n- κ p x 2 + y 2 + z 2 o . Express the answer in spherical coordinates. 2 The Electric Flux Through a Plane A charge distribution ρ ( r ) with total charge Q occupies a finite volume V somewhere in the half-space z < . If the integration surface is the plane z = 0, prove that Z z =0 dS ˆ z · E = 2 πQ. 3 Practice with Superposition A sphere of radius R 1 has charge uniformly distributed throughout its volume except for a smaller charge- free spherical volume of radius R 2 < R 1 located entirely within the big sphere. Show that the electric field at all points inside the small sphere is a constant....
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hw1 - 1 Phys6103 Homework set#1 1 Gauss’ Law Practice Use...

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