Answer to Question #136946 in Electrical Engineering for Teetly

Question #136946
For a cylindrical system, Prove that the electric field intensity at a point P located at a distance r from an infinite line charge with uniform charge density of ρL C/m is, E = ρ_L/(2π∈_0 r) a_r
Expert's answer

If "r\u2265R" , then the entire intensity vector flow will pass through the side surface of the cylinder, since the flow through both bases is zero. The cylinder side surface area formula is written as:

"2\\times \u03c0\\times r\\times l" . We will apply Gauss's law to a magnetic flux and we will receive:

"F=E\\times 2\\times\u03c0\\times r\\times l" , and as "E=\\frac{q}{4 \\times \u03c0 \\times \u03b5_0 \\times r^2}" , therefore "F=\\frac {\u03c1_L\\times l}{\u03b5_0}"

said expression A is a charge of the length of the cylinder. You can then write:

"E= \\frac {\u03c1_L} {2\\times \u03c0 \\times \u03b5_0 \\times r}" .

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