Homework Help: Flux of an infinite line of charge through a cylinder

1. The problem statement, all variables and given/known data

http://smartphysics.com/Content/Media/Images/EM/03/h3_lineD.png [Broken]

charge density 1 = .00029 C/m
charge density 2 = -.00087 C/m
h = .116 m
a = .094 m

a) What is the total flux Φ that now passes through the cylindrical surface of height h=.116 m? Enter a positive number if the net flux leaves the cylinder and a negative number if the net flux enters the cylinder.

b) The initial infinite line of charge is now moved so that it is parallel to the y-axis at x = -4.7cm (i.e. the two lines are equidistant from the center of the cylinder). What is the new value for Ex(P), the x-component of the electric field at point P?

c) What is the total flux Φ that now passes through the cylindrical surface? Enter a positive number if the net flux leaves the cylinder and a negative number if the net flux enters the cylinder.

2. Relevant equations

gauss' law

3. The attempt at a solution

a) How can we use Gauss' law? The magnitude of the field isn't uniform so it doesn't simplify.

b) This is easy enough, included as context for the next part.

c) The net flux should be the same as in part a) since the total charge flowing through the surface is the same.

 

I think I made some headway. For the first question the electric field is not constant over the suface nor is it everywhere perpendicular to dA so we can't use the flux = ∫E*DA half of Gauss' law. We can use the right side, i.e. flux = Qcontained/eo. Multiply each charge density by the height of the cylinder to get the total charge through each piece of rod contained by the cylinder. Then we can add them to get the net charge through the cylinder and lastly divide by the permittivity of free space constant to get the net flux, which will be negative.

Charge density1 = +.00029 C/m

Charge density2 = -.00087 C/m.

Q1 = (.00029)*(.116)
Q2 = (-.00087)*(.116)

Flux = (Q1+Q2)/eo

But apparently this is incorrect.

 

This problem is killing me. I just don't see how my approach could be incorrect. Anyone?