How Does Gauss's Law Apply to Electric Fields at Points P2 and P3?

[jesuslovesu]

[SOLVED] Gauss and E-Field

Homework Statement

http://img443.imageshack.us/img443/9452/eletroof9.th.png

My main problem with this problem is finding the electric field at Point 2 (P2)

Homework Equations

The Attempt at a Solution

I derived the electric field using Gauss's Law for a cylindrical charge distribution.
$$E (2\pi rL ) = \rho(\pi r^2 L) / \varepsilon_0$$
$$E = \frac{\rho * r}{2\varepsilon_0}$$
So I found E at P1 to be 0 V/m

Now onto finding E at P2, according to my equation, it would seem that E is 0, since the radial distance is 0, however that seems strange to me, if the point is at the surface of the charged volume cylinder, wouldn't there be some charge, I know it's not a conductor but still I would think that there would be some charge?And since I've got it all out here, is the E field at P3 just the integral [3/2L, L/2] of a charged disk?

 

[michalll]

The gausses law won't help you much here.
Try working with Ex = k*q*x/r^3.

 

[jesuslovesu]

Thanks for your reply,

I can't use Gauss's Law for finding any of the points? I know usually the cylinder is an infinite length if you want to find E, but even for Point 1 I can't use it?

 

[michalll]

Basically not in or outside finite length cylinder the tangential forces will cancel only at the midpoints. Try finding E on axis of a charged disc first.

 

[jesuslovesu]

Ok so I've got the equation for a charged disk
$$2\pi k \rho (1 - \frac{x}{\sqrt{x^2+a^2} ) }$$ how do I integrate that over the length (L) to get the electric field of the cylinder?

Would I say that dE = $$2\pi k \rho (1 - \frac{x}{\sqrt{x^2+a^2} ) }$$ and then integrate dE from 0 to L or do I need to differentiate Edisk before I do that?

 

[michalll]

Just integrate it form 0 to L, since ddQ = 2*pi*rho*a*da*dx and u integrated it along a then your equation should still contain dx.