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Answer to Question #42494 in Electricity and Magnetism for Scott
Question #42494
A solid cylinder of length L and radius R has a uniform charge density of rho "P". Calculate the electric field vector on the axis of the cylinder, a distance z from the center, and outside the cylinder.
ie: z > L/2
ie: z > L/2
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Comments
According to [url=https://en.wikipedia.org/wiki/Gauss%27s_law]Gauss law[/url], one can write 4*\pi*Q = \int E dS. Let us consider a cylindrical volume of radius r and length l with infinite thin charged thread on the axis. The total charge in this volume will be Q = \lambda*l where \lambda is a linear charge density. The surface area of the given volume is S = 2*\pi*r*l -- only through edge surface of this cylindrical volume the flux of E is nonzero. So, 4*\pi*\lambda*l = E * 2*\pi*r*l or E = 2*\lambda/r.
how did you get 2 λ / r ?
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