Electric Fields: Point Charges, Dipoles, Line Charges, and Continuous Distributions - Prof, Study notes of Physics

Download Electric Fields: Point Charges, Dipoles, Line Charges, and Continuous Distributions - Prof and more Study notes Physics in PDF only on Docsity! Lecture 18 • Chapter 27 (The Electric Field) due to configuration of (source) charges (today) parallel plate capacitor (uniform ) motion of (other) charges in Ē Ē Ē • good approx. for small charged object, real wire • Coulomb’s law • due to point charge • limiting cases (check + simpler formula): like point charge very far ( size) Electric Field Models Ē Ē ! K = 14!"0 " ! Electric Field of a Continuous Charge Distribution • even if charge is discrete, consider it continuous, describe how it’s distributed (like density, even if atoms • Strategy (based on of point charge and principle of superposition) divide Q into point-like charges find due to convert sum to integral: Ē !Q !Q !Q ! density "dx (x describes shape of !Q) Electric Field of a Line of Charge • Problem • Strategy • Solution...: Infinite line of charge:Eline = limL!" 14!"0 |Q| r ! r2+(L/2)2 = 14!"0 |Q| rL/2 = 1 4!"0 2|#| r Erod = 14!"0 |Q| r ! r2+(L/2)2 Review of Line of charge • due to segment i: • Sum over segments: • Relate to coordinate: • Sum to integral: Ex = Q/L4!"0 ! L/2 !L/2 rdy (r2+y2)3/2 !Q N !"; !y ! dy; !N i ! " L/2 !L/2 Ex = !N i (Ei)x = 1 4!"0 !N i r!Q (r2+y2i ) 3/2 Ex = Q/L4!"0 !N i r!y (r2+y2i ) 3/2 !Q = !!y = (Q/L) !y ! Ēi " x = 1 4!0 !Q r2i cos "i = 1 4!0 r!Q (r2 + y2i ) 3/2