Calculating Electric Field in a Line of Charge Problem

[Andrew.]

There lies a section through 2 long concentric cylinders of radii 4.5 and 8 cm. The cylinders have equal and opposite charges per unit length of 2 C/m. Along the common axis runs a wire with an equal positive charge per unit length. Find E at a radial distance r = 0.3 cm.

I'm not exactly sure how to complete this problem. I've calculated it ignoring the cylinders, thinking that their charges cancel each other out, yet this was still the incorrect answer. I've also tried this by adding up all of the forces from the cylinders at the point .3 cm, but yet this still didn't work! Any help would be greatly appreciated.

 

[gnome]

By Gauss's law, the cylinders will not produce any electrical field in the region inside the cylinders, regardless of the charges on the cylinders - equal, equal and opposite, different, whatever.

So you were right to ignore the cylinders (although for the wrong reason). Now the question is, how did you try to calculate the field?

 

[Andrew.]

I used the equation E = lambda / (2 * pi * epsilonknot * r)

With epsilonknot = 8.85 * 10^-12, and r = .003m

When I used it, however, I wasn't sure what value to use for lambda, the linear charge density, so I think the problem may lie in there.

Thank you very much, by the way. :)

 

[gnome]

The way I read it the charge on the wire is 2C/m, isn't it?

That gives a field of 1.2 x 10¹³N/C. Is that not the answer?

 

[Andrew.]

Ahh, I got it now! It turns out that that is indeed the answer. Thank you so very much! :)