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Lecture05

Lecture05 - 1 Lecture 5 Chapter 16 Electric Fields Overview...

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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 ˆ 4 1 2 1 1 πε = For a Point Charge: For a Dipole: for r>>s : E = 1 4 πε 2 qs r 3 ,0,0 at <r,0,0> E = − 1 4 πε qs r 3 ,0,0 at <0,r,0> x y z at <0,0,r> E = − 1 4 πε qs r 3 ,0,0 +q -q s Distributed Charges E ( x , y , z ) = 1 4 πε Q i r i 2 i = 1 N ∑ ˆ r i E ( x , y , z ) = 1 4 πε ρ ( x ', y ', z ') ˆ rdx ' dy ' dz ' r 2 ∫ ( x , y , z ) ( x ', y ', z ') ρ ( 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 Δ Q Line of charge: λ = charge per unit length [C/m] Δ q = λ Δ x Surface of charge : σ = charge per unit area [C/m 2 ] Δ q = σ dA = σ dxdy ( Cartesian coordinates) Volume of Charge : ρ = charge per unit volume [C/m 3 ] Δ q = ρ dV = ρ 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 Δ Q Step 3:Evaluate Δ E contribution from the infinitesimal charge element Step 4:Exploit symmetry as appropriate...
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Lecture05 - 1 Lecture 5 Chapter 16 Electric Fields Overview...

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