P23_025

# P23_025 - 25. Consider an inﬁnitesimal section of the rod...

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Unformatted text preview: 25. Consider an inﬁnitesimal section of the rod of length dx, a distance x from the left end, as shown in the diagram below. It contains charge dq = λ dx and is a distance r from P . The magnitude of the ﬁeld it produces at P is given by 1 λ dx . 4πε0 r2 1 λ dx sin θ The x component is dEx = − 4πε0 r2 1 λ dx cos θ . and the y component is dEy = − 4πε0 r2 dE = y dq x R . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. x r θ . • .. .. P .. .. . .. .. ... .... d E . ... We use θ as the variable of integration and substitute r = R/ cos θ, x = R tan θ and dx = (R/ cos2 θ) dθ. The limits of integration are 0 and π/2 rad. Thus, Ex = − π /2 λ 4πε0 R sin θ dθ = 0 and Ey = − λ 4πε0 R λ cos θ 4πε0 R π /2 0 =− λ 4πε0 R λ sin θ 4πε0 R π /2 0 =− λ . 4πε0 R π /2 cos θ dθ = − 0 We notice that Ex = Ey no matter what the value of R. Thus, E makes an angle of 45◦ with the rod for all values of R. ...
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## This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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