hw1_p5405_f02 - ,10 a What is the charge/length b What is...

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HW 1 Phys5405 f02 due Sept. 3 1a) A long wire that lies along the z axis carries a uniform current I in the z direction and gives rise to a magnetic induction B = μ 0 I 2 πρ e φ , where ρ is the radial vector in the xy plane. What is B in rectangular coordinates and unit vector? In spherical coordinates and unit vectors? 1b) The electric field due to an infinite line of charge with charge/length λ that lies along the z axis is, E = λ 2 π± 0 ρ e ρ . Write this field in cartesian coordinates and unit vectors and then repeat for spherical coordinates. 2) You will do parts a, b, c for 3 cases. case 1: 3 point charges q lie on the z axis at z = iL/2, i = 0,1,2 case 2: 6 point charges q lie on the z axis at z = iL/5, i = 0,1,2,. ..,5 case 3: 11 point charges q lie on the z axis at z = iL/10, i = 0,1,2.
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Unformatted text preview: ..,10 a) What is the charge/length, λ b) What is E (x=0,y=0,z=L+D) · (8 π± D )? Write answer in terms of λ instead of q. c) Specialize b) to the condition L=D and obtain a numerical answer. 3) A line of charge with uniform charge/length = λ lies along the z axis from z=0 to z=L. Repeat cases b) anc c) of problem 2 for this case. 4) A right cylindrical region of radius R has its axis along the z axis and extends from z = 0 to z = L. It carries uniform volume charge density ρ . Repeat parts a), b), c) of problem 2 for this problem. d) Let D >> R and D >> L, guess what the answer for the E is? Now show that the result you obtained in part b reduces to this answer for this condition. 1...
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