- #1

guyvsdcsniper

- 237

- 35

- Homework Statement:
- Find the potential V (x,y) at all points across the section of this pipe.

- Relevant Equations:
- dv/dx=0

I have attached an image of the pipe in the attachmnts. The pipe is parallel to z-axis form (-∞,∞) and sides of length a.

So my boundary conditions for this problem are as follows

1.) V=0 at y=0

2.)V=0 at y=a

4.)∂v/∂x=0 @ x=0

3.)V

I am a little confused on the fourth boundary condition only because my answer doesn't seem to match up with what I have found on the internet.

When solving B.C 4 and simplify i get, V

The answer I found gives V

Im not sure how they are getting the equation to be a multiple of 2 when the identity of (e

The solution I found is the image that looks scanned. My work is the image that is in blue and black ink.

So my boundary conditions for this problem are as follows

1.) V=0 at y=0

2.)V=0 at y=a

4.)∂v/∂x=0 @ x=0

3.)V

_{0}@ x=aI am a little confused on the fourth boundary condition only because my answer doesn't seem to match up with what I have found on the internet.

When solving B.C 4 and simplify i get, V

_{0}=Csin(nπy/a)(cosh(nπ)/2)The answer I found gives V

_{0}=2Csin(nπy/a)(cosh(nπ))Im not sure how they are getting the equation to be a multiple of 2 when the identity of (e

^{x}+e^{-x})=cosh(x)/2The solution I found is the image that looks scanned. My work is the image that is in blue and black ink.