Consider the electric field ๐ธ = ๐๐
๐๐๐
4๐๐0
โซ
๐๐ง
โฒ
(๐
2+๐งโฒ
2)
3/2
+โ
โโ
due to the uniform line charge density ฯl
= 12 ยตC/m of an infinitely long straight conducting wire at a distance r. Find out the numeric value ofย
r. Remember that prime variables corresponds to the source quantity.
Given,
Electric field "E=ar"
"E=\\frac{r\\rho l}{4\\pi \\epsilon_o}\\int_{-\\infty}^{\\infty} \\frac{dz}{(r^2+z^2)^{3\/2}}"
"=\\frac{ar\\rho l}{4\\pi \\epsilon_o}\\times [\\frac{z}{r^2(z^2+r^2)}]_{-\\infty}^{\\infty}"
"=\\frac{ar\\rho l}{4\\pi \\epsilon_o}\\times (\\frac{2}{r^2})"
So,
"ar=\\frac{r\\rho l}{4\\pi \\epsilon_o}\\times (\\frac{2}{r^2})"
"\\Rightarrow" "r=\\sqrt{\\frac{2\\rho l}{4\\pi \\epsilon_o a}}"
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