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

1. Sep 3, 2011

### blueyellow

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

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)

3. 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

2. Sep 3, 2011

### Staff: Mentor

Re: using Gauss' theorem ande exploiting the cylindrical symmetry of the system, show

Plug in for the given value of r.

3. Sep 3, 2011

### blueyellow

Re: using Gauss' theorem ande exploiting the cylindrical symmetry of the system, show

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?

4. Sep 3, 2011

### Staff: Mentor

Re: using Gauss' theorem ande exploiting the cylindrical symmetry of the system, show

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.