MIT6_641s09_sol_quiz2006_1

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Unformatted text preview: T= 4 q2 2π 3 d3 ε0 m q2 Problem 2 y λ -L I ε0 + + + + + + +++++++ +++++++ a II φ III -a a L x Figure 2: Uniformly distributed line charge λ. (Image by MIT OpenCourseWare.) Φ(r ) = l′ λ(r ′ )dl′ 4π ε0 |r − r ′ | E (r ) = l′ λ(r ′ )ir′ r dl′ 4π ε0 |r − r ′ | 2 A Question: Find the p otential at the p oint (x = 0, y = 0, z = 0) −a Φ(x = 0, y = 0, z = 0) = x =− L −a π λ = − ln x + φ + ln x 4 π ε0 −L 0 L a λ − ln + π + ln = = 4 π ε0 L a λdx + 4π ε0 (−x) π φ=0 λadφ + 4 π ε0 a L a L x =a λdx 4π ε0 (x) λ 4π ε0 (π + 2 ln L ) a B Question: Find the electric ﬁeld (magnitude and direction) at (x = 0, y = 0, z = 0). 3 Spring 2006 Quiz 1 Solution: −a 6.641, Spring 2005 E (x = 0, y = 0, z = 0) = x =− L λix dx + 4π ε0 x2 −a π φ=0 π λ(−ir )adφ + 4 π ε 0 a2 L x=a λ(−ix )dx...
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This note was uploaded on 12/02/2010 for the course ECE 6.641 taught by Professor Zahn during the Spring '09 term at MIT.

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