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# Answer to Question #42494 in Electromagnetism for Scott

Question #42494
A solid cylinder of length L and radius R has a uniform charge density of rho &quot;P&quot;. Calculate the electric field vector on the axis of the cylinder, a distance z from the center, and outside the cylinder. ie: z &gt; L/2

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Assignment Expert
17.05.14, 10:39

According to Gauss law, 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.

guest
17.05.14, 04:36

how did you get 2 λ / r ?