Electric Field Integration Outside a Cylinder

[frostmephit]

Homework Statement

A thin, hollow cylinder missing its two end caps is shown to have a charge of -90nC. It has a radius of .5 cm and is 2.0 cm long. Find the charge on an $$\alpha$$ particle 5.0cm away from the end of the cylinder closest to the particle. (The center of the cylinder is on the same axis as the alpha particle.)

Homework Equations

(Electric Field of a Ring)
E=1/(4$$\pi\epsilon$$$$\o$$) * q$$\Delta$$z/(R^2+$$\Delta$$z^2), where R is the radius of the cylinder and z is the distance from the center of the ring to the observation location, q is the charge, and the charge of an alpha particle is given by 2e

The Attempt at a Solution

The way I have gone about doing this is in such a manner as to divide the cylinder up into so many small rings, each with an infinitesimaly small charge. The problem is, I can't figure out how to create an equation representing the whole cylinder. I am aware that the charge on the rings would be equal to the surface area of one of them divided by the surface area of the greater cylinder times the charge, but I've been having trouble representing this as an equation for integration. Am I going in the right direction, and could someone please help?

 

[Redbelly98]

Welcome to Physics Forums.

Homework Equations

(Electric Field of a Ring)
E=1/(4$$\pi\epsilon$$$$\o$$) * q$$\Delta$$z/(R^2+$$\Delta$$z^2), where R is the radius of the cylinder and z is the distance from the center of the ring to the observation location, q is the charge, and the charge of an alpha particle is given by 2e

The Attempt at a Solution

The way I have gone about doing this is in such a manner as to divide the cylinder up into so many small rings, each with an infinitesimaly small charge. The problem is, I can't figure out how to create an equation representing the whole cylinder. I am aware that the charge on the rings would be equal to the surface area of one of them divided by the surface area of the greater cylinder times the charge, but I've been having trouble representing this as an equation for integration. Am I going in the right direction, and could someone please help?

Okay. First, I'll recommend using z instead of Δz, for the distance from the alpha particle to the ring.

If each ring has a "length" of dz along the z-direction, what would be the charge q on that ring? You're expression for q should contain a "dz" in it, so that will (hopefully) suggest an integral.