Question

Hi, another cylinder question. How do I find the electric field at a point vertically above a standing solid uniformly charged cylinder?

Answer 1

Since, the cylinder seems finite, so you could divide the cylinder into small disks each ahving width dl, and calculate the field at the centre of one disk and integrate it.

Answer 2

Use Gauss' law with a cylindrical gauusian surface larger than the diameter (radius R) of the real cylinder. Then calculate the close surface integral: E*Area(gaussian)=sigma*A(real cylinder)/e -> E*2*pi*R*h=sigma*2*pi*r*h/e, where sigma is the surface charge density and e is the permittivity constant of free-space, R is the radius of the Gaussian cylinder, r the radius of the real cylinder and h the height of the real cylinder and gaussian surface. so E=sigma*r/Re. "r" is a point above the cylindrical surface.

Answer 3

@ybarrap : What you're suggesting is the basic Gauss' Law for cylinders- E=sigma*r/(epslon*R). It can be calculated for a point at a certain distance from the axis of the cylinder; not above- because for easy application of the Gauss' Law symmetry is required. Moreover the cylinder here has been said to be solid. So It shall have a volume charge density, not surface charge density- sigma

Answer 4

You're right. I thought about that later, that this was not a conductor and if E above caps of cylinder is needed, your approach would be needed because there is no way to exploit symmetry with Gauss' Law. Good catch.