# Calculate the electostatic field outside a finite cylinder

• A
Hello,

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

kuruman
Homework Helper
Gold Member
2021 Award
There was a recent discussion about the E(r) in the plane of a charged ring. The integrals involved were complicated enough. Your question seems to be even more complicated because one way to proceed after solving the ring problem is to assemble a disk from many rings and then a cylinder from many disks. You might also try a multipole expansion of the potential and then take derivatives.

https://www.physicsforums.com/threa...-of-a-ring-of-charge-in-the-x-y-plane.950299/

There was a recent discussion about the E(r) in the plane of a charged ring. The integrals involved were complicated enough. Your question seems to be even more complicated because one way to proceed after solving the ring problem is to assemble a disk from many rings and then a cylinder from many disks. You might also try a multipole expansion of the potential and then take derivatives.

https://www.physicsforums.com/threa...-of-a-ring-of-charge-in-the-x-y-plane.950299/
Hello,
I will try to use this informations to solve my problem. A big thanks !

Palaj