b.Electric Field from a Sheet Charge d=cndx (x2+y2)1/2 dE=dE,+dE2 26 (a) (b) 个do=Pody Po 川 Poa 280 →y dE=- 2 0 (c) (a)The electric field from a uniformly surface charged sheet of infinite extent is found by summing the contributions from each incremental line charge element.Symmetrically placed line charge elements have x field components that cancel,but y field components that add.(b)Two parallel but oppositely sheets of surface charge have fields that add in the region between the sheets but cancel outside.(c)The electric field from a volume charge distribution is obtained by summing the contributions from each incremental surface charge element. d dEy = C0s0= coydx 2(x2+y2 2πeo(x2+y2] -I t dx x2+y2 6.641,Electromagnetic Fields,Forces,and Motion Lecture 3 Prof.Markus Zahn Page 9 of 126.641, Electromagnetic Fields, Forces, and Motion Lecture 3 Prof. Markus Zahn Page 9 of 12 ( ) ( ) 0 y 1 2 2 2 2 2 0 0 d ydx dE cos 2 xy 2 xy λ σ = θ = π + π + ε ε 0 y y 2 2 0 x x y dx E dE 2 x y +∞ +∞ = −∞ = −∞ σ = = πε + ∫ ∫ 0 1 0 y 1 x tan 2y y +∞ − −∞ σ = πε b. Electric Field from a Sheet Charge