problemset3

a q n b figure 8 figure for 32 d field lines from

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Unformatted text preview: (y + h)2 + z 2 ] 2 where q is the charged bird modeled as a point charge. D By boundary condition found using Gauss’ Law → −a →b − → −b n · (εa E − εb E ) = σs at the y = 0 ground plane boundary where E = 0. ˆ 5 Problem Set 3 6.641, Spring 2009 y +q bird at (Ut, h, z) Φ=0 on xz-plane x z -q image at (Ut, -h, z) Figure 7: Figure for 3.2 B, C. Method of Images for charged bird taken as a point charge flying over a ground plane (Image by MIT OpenCourseWare.) a q n b Figure 8: Figure for 3.2 D. Field lines from point charge above a perfectly conducting ground plane (Image by MIT OpenCourseWare.) → −a Because we can consider the ground plane to be a perfect conductor, n · E = ˆ σs ε0 . σs → → − − (ˆy ) · ( E (x, y = 0+ , z )) = i implies we only care about the y component of E ε0 Ey (x, y = 0+ , z ) = σs ε0 � ∂ q Ey = − Φ = ∂y 4πε0 (1) (y − h) 3 [(x − U t)2 + (y − h)2 + z 2 ] 2 Evaluate at y = 0 and substitute into (1) above: � � −2h q Ey (x, y = 0, z ) = 4πε0 [(x − U t)2 + h2 + z 2 ] 3 2 6 − � (y + h) 3 [(x − U t)2 + (y + h)2 + z 2 ] 2 Problem Set 3 6.641,...
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