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Unformatted text preview: Test I Physics 351 Oct. 12, 98 Dr. Gangopadhyaya As always, to receive full credit you must show your work in a neat, organized and a legible form. Partial credit will be given only for well deserving work. Do not write answer to more than one problems in one sheet. When done, put problems in ascending order and staple all pages. 1) A charge Q is distributed uniformly along a curve in such a way that its volume charge density has following properties: ρ ( ~ r ) = r > R r < R θ > π 6 θ < π 6 (1) • a) Express the volume charge density as a function of ( r, θ, φ ) in a compact form using Dirac- δ function; • b) draw a 3-D diagram to show the charge distribu- tion; • c) show that the volume integration of this charge density over all space indeed gives the total charge Q. 1 2a) Determine the electric field due to a uniformly charged ring of radius ‘ r ’ and charge ‘ q ’, at a point P on its axis ....
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