Lecture_06_(Chap.16) - Register your clicker if you havent...

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• Register your clicker if you haven’t done it. • No lecture this Wednesday, Feb. 2. • Exam 1 on Feb 15 (Tuesday), 8-9:30 PM, 1
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E of Uniformly Charged Thin Rod In vector form: E y 0 1 4  0 Q rr 2 L /2 2 ˆ r At center plane Check the results: Direction Units Special case r >> L: E y 0 1 4 Q r 2 ˆ r 0 Special case 2: L >> r (very long rod) E y 0 1 4 0 2 Q / L r ˆ r 1/ r dependence! Q / L – linear charge density 2
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E of Uniformly Charged Rod At distance r from midpoint along line perpendicular to the rod: a line perpendicular to the rod: 1 Q ˆ E y 0 4  0 rr 2 L /2 2 r l d For very long rod: E 1 2 Q / L ˆ r 4 0 r Field at the ends: Numerical calculation 3
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General Procedure for Calculating Electric ield of Distributed Charges 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 pp (i) Try to integrate symbolically (ii) If impossible – integrate numerically 4. Check the results: (i) Direction (ii) Units (iii) Special cases 4
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rigin: nter of the ring A Uniformly Charged Thin Ring Origin: center of the ring Location of piece: described by θ , where θ = 0 is along the x axis. Step 1: Cut up the charge distribution into small pieces tep 2: rite ue to one piece Step 2: Write E due to one piece source loc obs r . 0 , sin , cos , 0 , 0 R R z r z R R r , sin , cos  r R cos  2 R sin 2 z 2 R 2 cos 2  2 z 2 r R 2 z 2 ˆ r R cos , R , z R 2 z 2 5
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A Uniformly Charged Thin Ring Step 2: Write dE due to one piece 2 2 z R r d dQ Q   ˆ r R cos , R sin , z 2 2 2  R z cos , sin , 1 R Rz dQ E    22 0 4 dE  1 s sin Q d E R R z 3/2 0 cos , , 42 dE  6
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A Uniformly Charged Thin Ring Step 2: Write Δ E due to one piece 1 s sin Q R R z   3/2 22 0 cos , , 42 ER Rz    1 s QR E d  Components:   0 cos x dE   /2 1 sin dE d   0 y R z 1 Qz dE d   0 z 7
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A Uniformly Charged Thin Ring Step 3:
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This note was uploaded on 04/23/2011 for the course PHYS 272h taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

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Lecture_06_(Chap.16) - Register your clicker if you havent...

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