electric field of a line charge from Columbus law
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Explanation:
This might seem naive or have a trivial resolution, but I'm still searching for one and have been unable to find it.
Consider an infinitely long line charge with uniform line charge density λ. The electric field at any point in space is easily found using Gauss's law for a cylinder enclosing a portion of the line charge. The correct result is
Er=λ2πϵ0r.
However, if you use the Coulomb law
14πϵ0∫∞−∞λdxx2+r2
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