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Unformatted text preview: 1 Lecture 5 Chapter 16 Electric Fields * Overview * A Uniformly Charged Thin Rod * General Procedure for Calculating Electric Field Previous Lectures..Discrete Charges r r q E 4 1 2 1 1 = For a Point Charge: For a Dipole: for r>>s : E = 1 4 2 qs r 3 ,0,0 at <r,0,0> E = 1 4 qs r 3 ,0,0 at <0,r,0> x y z at <0,0,r> E = 1 4 qs r 3 ,0,0 +q -q s Distributed Charges E ( x , y , z ) = 1 4 Q i r i 2 i = 1 N r i E ( x , y , z ) = 1 4 ( x ', y ', z ') rdx ' dy ' dz ' r 2 ( x , y , z ) ( x ', y ', z ') ( x ', y ', z ') 1/25/11 4 How do we represent the charge Q on an extended object? total charge Q small pieces of charge Q Line of charge: = charge per unit length [C/m] q = x Surface of charge : = charge per unit area [C/m 2 ] q = dA = dxdy ( Cartesian coordinates) Volume of Charge : = charge per unit volume [C/m 3 ] q = dV = dx dy dz (Cartesian coordinates) Charge Densities 2 1/25/11 5 Calculate E-field due to charge distributions 1/25/11 6 Charge Distributions Problems Step 1:Understand the geometry Step 2:Choose Q Step 3:Evaluate E contribution from the infinitesimal charge element Step 4:Exploit symmetry as appropriate...
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