# V of 2 parallel lines makes cylinders

1. Sep 16, 2013

### bowlbase

1. The problem statement, all variables and given/known data
Expanded from Griffith's (3rd ed) #2.47

Infinitely long wires parallel to x axis carrying ±λ charge densities intersect the y-axis at ±a.

A) Calculate V(x,y,z) if V(0,0,0)=0
B)Show that the equipotential surfaces are circular
cylinders. Locate the axis and calculate the
radius of the cylinder that is at potential V0.

2. Relevant equations
Gauss, -∫Edl
E=-∇V
?x2+y2=r2?

3. The attempt at a solution

I've found the solution to part A easily enough but I'm not sure how to approach B. I know that at the origin the potential is zero along the x axis but I'm confused by how I should show that these are both circular cylinders.

I'd post my solution for A but it's exactly the same as the solution manual so it's easy enough to find.

Any help would be appreciated.

2. Sep 16, 2013

### Bryson

Why not look at your solutions manual. . .

3. Sep 16, 2013

### bowlbase

The part b is not part of the original question. Thus, not in the manual.

4. Sep 17, 2013

### bowlbase

hmm, never mind I guess it was in the manual. Sorry thought that he just added it. thanks anyway.