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F07_hw01 - 2 × 10-11 F/m if the separation of the wires...

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Physics 505 Fall 2007 Homework Assignment #1 — Due Thursday, September 13 Textbook problems: Ch. 1: 1.5, 1.7, 1.11, 1.12 1.5 The time-averaged potential of a neutral hydrogen atom is given by Φ = q 4 π 0 e - αr r 1 + αr 2 where q is the magnitude of the electronic charge, and α - 1 = a 0 / 2, a 0 being the Bohr radius. Find the distribution of charge (both continuous and discrete) that will give this potential and interpret your result physically. 1.7 Two long, cylindrical conductors of radia a 1 and a 2 are parallel and separated by a distance d , which is large compared with either radius. Show that the capacitance per unit length is given approximately by C = π 0 ln d a - 1 where a is the geometrical mean of the two radii. Approximately what gauge wire (state diameter in millimeters) would be necessary to make a two-wire transmission line with a capacitance of 1
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Unformatted text preview: . 2 × 10-11 F/m if the separation of the wires was 0.5 cm? 1.5 cm? 5.0 cm? 1.11 Use Gauss’s theorem to prove that at the surface of a curved charged conductor, the normal derivativce of the electric field is given by 1 E ∂E ∂n =-³ 1 R 1 + 1 R 2 ´ where R 1 and R 2 are the principal radii of curvature of the surface. 1.12 Prove Green’s reciprocation theorem : If Φ is the potential due to a volume-charge density ρ within a volume V and a surface-charge density σ on the conducting surface S bounding the volume V , while Φ is the potential due to another charge distribution ρ and σ , then Z V ρ Φ d 3 x + Z S σ Φ da = Z V ρ Φ d 3 x + Z S σ Φ da...
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