Using Gauss' theorem ande exploiting the cylindrical symmetry of the system, show

[blueyellow]

Homework Statement

A wire of length L and negligible transverse dimensions, made of an insulating material, is placed on the x-axis between the origin and the point (L,0). The wire has a uniform line charge density lambda.

using Gauss' theorem and exploiting the cylindrical symmetry of the system, show that the electric field at the point (x,y)=(L/2,L/100) is

E=(100lambda)/(2pi epsilon0 L)

The Attempt at a Solution

integral (S) E.da=E 2 pi r l
Q/(epsilon 0)=(lambda l)/(epsilon0)

2pi r l E=lambda l/epsilon0

E=(1/2 pi r l) (lambda l/epsilon0)
=lambda/(2 pi epsilon0 r)

but I don't know how to proceed from here

 

[Doc Al]

Plug in for the given value of r.

 

[blueyellow]

oh right! so r is just L/100 because it the wire is along the x axis, so I don't have to do L-L/2?

 

[Doc Al]

oh right! so r is just L/100 because it the wire is along the x axis, so I don't have to do L-L/2?

Right. The point where you want to evaluate the field is at a distance of L/100 from the wire, so that's the value of r you need to use.