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heartofaragorn

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## Homework Statement

Two coaxial cylindrical conductors are shown. The inner cylinder has radius a = 2 cm, length 10 m, and carries a total charge of Q inner = +8nC. The outer cylinder has an inner radius b = 6 cm, outer radius c= 7 cm, length 10 m, and carries a total charge of Q outer = -16nC. What is Ex, the x-component of the electric field at point P which is located at the midpoint of the length of the cylinders at a distance r= 4 cm from the origin and makes an angle of 30 degrees with the x-axis?

## Homework Equations

Surface charge density = 2pi * radius a * length

Linear charge density = 2pi * radius a * surface charge density

Electric field = 2 * k * linear charge denisty / r

## The Attempt at a Solution

I drew a Gaussian sphere at the radius r = 4 according to where point P lies and tried to determine the charge inside, which I think may be where I went wrong. There is an enclosed cylinder of +8 nC that has a radius of 2 that falls completely within the Gaussian sphere; however, I cannot see that the outer charge affects this particular sphere since it is within the 2nd cylinder. I calculated the surface charge density to be 2.5133 using the radius of 0.04 m, then plugged that into the linear charge density formula to receive an answer of 0.63165. I then tried plugging that into the formula for the electric field given by my prof and received an answer of 2.84245 e 11. I took that and mulitplied by cos 30 degrees to account for the diagnol line upon which P lies. I cannot get the right answer (interactive online problem) and I'm getting the feeling that I'm either using the wrong charge, wrong radius, or wrong formulae...or a combination of all 3! Please help me! Thanks!