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I am looking for an expression to calculate the electrostatic field outside a uniformly charged cylinder, radius R and finite length L. What interests me most is the radial field, E(r) in the plane z = L / 2. I found an expression of the potential V (r) in the case where L <<< R which involves the Legendre polynomials, but the integration is difficult. This particular case (L tends to 0) is sufficient.

Any help to move me forward would be very appreciated!

Thank you in advance for this help,

Palaj