Question

A long, uniformly charged ribbon is located in the xz plane, parallel to the z axis, occupying the region-o Zoo and -a/2sx a/2. The charge per unit arca on the ribbon is o (a) Determine E at (x, 0, 0), where x > a/2. What is the asymptotic field on the x axis? (b) Determine E at (O, y, 0), where y > 0. What is the asymptotic field on the y axis?

Answer 1

5 (a) r^16 rightarrow = x^1 i^+ z^1 R^r^rightarrow = x^r^rightarrow - e^rightarrow - z^1 b^r^rightarrow = x i^rightarrow^rightarrow (r^right arrow) = 1/ 4 pie epsilon integral^infin_-infin integral^a/2_-a/2 sigma dx^1 dz6 [(X-X^1) I^- Z^1k^]/ [(X-X^1)^2 + 2^12]^63/2 1/4pie epsilon integral^x + a/2_x- a/2 d epsilon integral^infin_- infin sigma d2^1 (epsilon i^- 2^1 k^/(epsilon^2 + 2 62)^3/2 where;x-x61 = epsilon = 1/1pie epsilon_o integral^_x-a/2 epsilon d epsilon integral^pie/2_pie /2 cos theta .d theta/epsilon^2 by 2^1 = epsilon tan theta.// note: integral^infin_-infin z^1d2^1/(epsilon 62 + z^12)^3/2 = 0: integrand is add in Z^1 E6rught arrow (r6right arrow) = sigma/2pie epsilon