# V of 2 parallel lines makes cylinders

• bowlbase
In summary, the conversation discussed a homework problem involving infinitely long wires with ±λ charge densities intersecting the y-axis at ±a. Part A asked for the calculation of V(x,y,z) with the given condition and the solution was easily found. Part B was not originally part of the question and asked for the proof that the equipotential surfaces are circular cylinders, as well as determining the axis and radius of the cylinder at potential V0. The manual did not have a solution for this part.

## Homework Statement

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.

Gauss, -∫Edl
E=-∇V
?x2+y2=r2?

## 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.

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

Why not look at your solutions manual. . .

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

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