hw1_p5405_f04 - ..,5 case 3: 11 point charges q lie on the...

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HW 1 Phys5405 F04 due Sept. 2 1) Obtain the velocity v = d r /dt = ˙r and acceleration a = d v /dt = ˙v in cylindrical coordinates. Recall in cartesian coordinates these are, v = ˙ x e x + ˙ y e y + ˙ z e z a = ¨ x e x + ¨ y e y + ¨ z e z In other coordinate systems only the appropriate coordinates and unit vectors should appear. 2) Obtain the divergence and curl of any vector A that is a function of position in spherical coordinates. Obtain the Laplacian of a scalar function of position in shpherial coordinates. 3) Prove ∇ × ( A × B ) = B ( ∇ · A ) - ( ∇ · A ) B + ( B · ∇ ) A - ( A · ∇ ) B 4) Prove R V dV ( f ) = H S da ( f n ), where f is a scalar function of coordinates. 5) You will do parts a and b 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,.
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Unformatted text preview: ..,5 case 3: 11 point charges q lie on the z axis at z = iL/10, i = 0,1,2. ..,10 a) What is the charge/length, λ b) What is E (x=0,y=0,z=L+D) · (8 π± D )? Write the answer in terms of λ instead of q. c) A line of charge with uniform charge/length = λ lies along the z axis from z=0 to z=L. Repeat case b) for this condition. d) 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) and b) for this condition. e) In 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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This note was uploaded on 12/24/2011 for the course PHYS 5406 taught by Professor Blecher during the Spring '10 term at Virginia Tech.

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