Electric field in cylinder with missing section

[hawaiigurl123]

Homework Statement

A uniformly charged, non-conducting, infinitely long cylinder of radius A is parallel to the z-axis, and its central axis intersects the x-y plane at the origin. It has a charge density p (C/m^3). Material is removed from the cylinder leaving a cylindrical void of radius A/2 running parallel to the z-axis, but its central axis intersects the x-y plane at the point x = A/2, y =0. Calculate the electric field at the points x = 0, x = A/4, x = A/2, and x = A.

Homework Equations

flux = E A cos(theta)
total charge = (p)(volume)
flux = total charge/e0
area of cylinder cross section before removal: piA^2
area of void cross section: (piA^2)/4
area of cylinder cross section after removal: (3piA^2)/4

The Attempt at a Solution

We're working on Gauss's Law in class so I'm guessing I'm supposed to use that, and I think I understand how to do this if a section wasn't missing, but I have no idea how to take into account the off-center missing section.

Thanks!

 

[Doc Al]

Hint: You can cancel a positive charge by adding a negative charge.

What kind of negative charge would you need to add to produce the given charge distribution with its missing section?

 

[hawaiigurl123]

I'm not sure I understand...
You mean, in order to keep p of the area as a whole constant before and after material is removed?

 

[Doc Al]

Here's what I'm getting at. Finding the field from a solid cylinder (or two solid cylinders) is easy. But having a missing piece makes it hard. So see if you can model the charge distribution with the missing piece as being composed of two solid cylinders, one of which happens to be negatively charged.

 

[hawaiigurl123]

I think I got it now. thanks a lot!