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Lecture06

Lecture06 - Electric Field of Uniformly Charged Thin Rod At...

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1 Electric Field of Uniformly Charged Thin Rod At distance r from midpoint along a line perpendicular to the rod: E y = 0 = 1 4 πε 0 Q r r 2 + L / 2 ( ) 2 ˆ r And for very long rod: E = 1 4 0 2 Q / L ( ) r ˆ r At distance r from an arbitrary location not at the midpoint : Δ E x = 1 4 o x Δ Q x 2 + ( y 0 y ) 2 3/2 Δ E y = 1 4 o y o y ( ) Δ Q x 2 + ( y 0 y ) 2 3/2 Δ E z = 0 General Procedure for Calculating Electric Field of Distributed Charges 1. Cut the charge distribution into pieces for which the field is known 2. Write an expression for the electric field due to one piece (i) Choose origin (ii) Write an expression for Δ E and its components 3. Add up the contributions of all the pieces (i) Try to integrate symbolically (ii) If impossible – integrate numerically 4. Check the results: (i) Direction (ii) Units (iii) Special cases Lecture 6 Chapter 16. Electric Fields * Uniformly Charged Thin Ring * Uniformly Charged Disk * Two Uniformly Charged Disks: A Capacitor Origin: center of the ring Location of piece: described by θ , where = 0 is along the x axis. Step 1: Cut up the charge distribution into small pieces. (i.e., understand geometry and choose Δ Q. ) A Uniformly Charged Thin Ring
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2 source loc obs r = .
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Lecture06 - Electric Field of Uniformly Charged Thin Rod At...

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