# L04 - Lecture 4 Total Charge Line Surface and Volume...

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LECTURE 4 slide 1 Lecture 4 Total Charge: Line, Surface and Volume Integrals Sections: 1.8, 1.9, 2.3 Homework: D2.4; 1.23, 1.27, 2.14, 2.16

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LECTURE 4 slide 2 Line Elements – 1 metric increment due to the differential increment of a coordinate a b d l x dx a y dy a x y d d dx y =+ l a a ρ a d φ a d a d ρφ a d d d = + l a a d l x a y a a b
LECTURE 4 slide 3 Line Elements – 2 line increment is a vector has direction: point of integration moves from point a to point b each of its components is a linear increment (in meters) RCS: dx , dy , and dz are linear by default CCS: d ρ and dz are linear, d φ is not SCS: dr is linear, d θ and d φ are not example: angular increment d φ corresponds to linear increment ρ d φ

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LECTURE 4 slide 4 r a φ a θ a d r dr rd d l sin r sin rd θφ d x y z Line Elements – 3 CCS: z dd d d z ρφ ρ =+ + la aa SCS: sin r r r d r d + a a
LECTURE 4 slide 5 the direction of integration does not matter: charge is scalar Line Integration: Charge on Lines – 1 B l A Qd l ρ = straight line: choose RCS axis along charged line SPECIAL CASES: CHARGE ON COORDINATE GRID LINES () B A x l x Qx d x = φ -line in CCS: circular charges in the x -0- y plane 0 B A l φ φρ =⋅ θ -line and φ -line in SCS 0 B A l Qr d θ θθ 00 () s i n B A l d φθ

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LECTURE 4 slide 6
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## This note was uploaded on 02/29/2012 for the course PHYS 227 taught by Professor Rabe during the Fall '08 term at Rutgers.

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L04 - Lecture 4 Total Charge Line Surface and Volume...

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