notes7 2317

# notes7 2317 - Coulombs Law ECE 2317 Applied Electricity and...

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Prof. Filippo Capolino ECE Dept. Fall 2006 Notes 7 ECE 2317 ECE 2317 Applied Electricity and Magnetism Applied Electricity and Magnetism Notes prepared by the EM group, University of Houston . (used by Dr. Jackson, spring 2006) Coulomb Coulomb ’s Law s Law x y z r q 1 q 2 r ± [] 12 2 2 0 12 0 N 4 8.854187818 10 F/m qq Fr r πε ε = ± Experimental law: Note: c = speed of light = 2.99792458 × 10 8 [m/s] (exactly) 00 1 c με = [ ] 7 0 41 0H / m( e x a c t l y ) μπ Coulomb Coulomb ’s Law (cont.) s Law (cont.) Hence: But 2 2 0 4 F r r = ± 1 1 2 0 4 q Er r = ± ( E 1 : E due to q 1 ) ( ) 2 22 1 F qE r = Note: no self-force on charge 2 due to its own electric field x y z r q 1 q 2 r ± Generalization ( q 1 not at the origin): Coulomb Coulomb ’s Law (cont.) s Law (cont.) r 1 = ( x 1 , y 1 , z 1 ) q 2 ( x 2 , y 2 , z 2 ) x y z R l R r 2 r 1 q 1 ( x 1 , y 1 , z 1 ) r 2 = ( x 2 , y 2 , z 2 ) () 21 1 222 2 RRrr xx yy zz ==− =−+ −+ l 1 1 2 0 4 q ER R = l R R R = R rr =−

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Example Example q 1 =0.7 [mC] located at (3,5,7) [m] q 2 =4.9 [ μ C] located at (1,2,1) [m] R q 2 q 1 E 1 = electric field due to charge q 1 , evaluated at point r 2 22 1 Fq E = Find: F 1 , F 2 For F 2 : F 1 = force on charge q 1 F 2 = force on charge q 2 Example (cont.) Example (cont.) l ± () ± ± ± ()()() l ± ± 1 1 2 0 21 222 4 13 25 17 236 7 [ m ] 777 q ER R Rr r x y z Rx y z RR R Rxyz R ± ± ± πε = =−= −+ −+ − =−+−+− ==−+ −+ − = −−− ⎛⎞⎛⎞⎛⎞ == + + ⎜⎟⎜⎟⎜⎟ ⎝⎠⎝⎠⎝⎠ R q 2 q 1 1
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notes7 2317 - Coulombs Law ECE 2317 Applied Electricity and...

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