HW_6 Solutions - Physics 2213 22.31. HW #6 Solutions Fall...

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Physics 2213 HW #6 Solutions Fall 2009 22.31. IDENTIFY: Apply Gauss’s law and conservation of charge. SET UP: 0 E = in a conducting material. EXECUTE: (a) Gauss’s law says + Q on inner surface, so 0 E = inside metal. (b) The outside surface of the sphere is grounded, so no excess charge. (c) Consider a Gaussian sphere with the – Q charge at its center and radius less than the inner radius of the metal. This sphere encloses net charge – Q so there is an electric field flux through it; there is electric field in the cavity. (d) In an electrostatic situation 0 E = inside a conductor. A Gaussian sphere with the Q charge at its center and radius greater than the outer radius of the metal encloses zero net charge (the Q charge and the Q + on the inner surface of the metal) so there is no flux through it and 0 E = outside the metal. (e) No, 0 E = there. Yes, the charge has been shielded by the grounded conductor. There is nothing like positive and negative mass (the gravity force is always attractive), so this cannot be done for gravity. EVALUATE: Field lines within the cavity terminate on the charges induced on the inner surface. 22.48. IDENTIFY: Apply Gauss’s law. SET UP: Use a Gaussian surface that is a sphere of radius r and that is concentric with the sphere and shell. The volume of the insulating shell is ( ) 33 3 4 28 [2 ] V RR R π = −= . EXECUTE: (a) Zero net charge requires that 3 28 3 π ρR Q , so 3 28 Q ρ πR 3 = − . (b) For , 0 r RE <= since this region is within the conducting sphere. For 2 , 0, >= since the net charge enclosed by the Gaussian surface with this radius is zero. For 2 Rr R << , Gauss’s law gives 2 00 4 (4 ) ( ) 3 Q πρ E πr r R = +− PP and 22 () 43 Q ρ E rR πr r = . Substituting ρ from part (a) gives 23 0 0 2 . 7 28 Q Qr E π r πR = P P The net enclosed charge for each r in this range is positive and the electric field is outward.
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This note was uploaded on 12/25/2009 for the course PHYS 213 at Cornell University (Engineering School).

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HW_6 Solutions - Physics 2213 22.31. HW #6 Solutions Fall...

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