- #1

physicsisfun0

- 2

- 0

## Homework Statement

We have the cross section of a metal pipe that has been split into four sections. Three of the sections have a constant electric potential, V

_{o}. The fourth section is grounded so electric potential is zero. We are looking for electric potential inside and outside of the pipe.

## Homework Equations

For electric potential I have:

V = a

_{o}+ b

_{o}ln(s) +Σ(s

^{v}(a

_{v}cos(vφ) + b

_{o}sin(vφ)) + s

^{-v}(c

_{v}cos(vφ) + d

_{v}sin(vφ))

We also know boundary conditions:

## The Attempt at a Solution

(I think this next part is right)

And electric potential inside becomes:

V = a

_{o}+ b

_{o}ln(s) +Σ(s

^{v}(a

_{v}cos(vφ) + b

_{o}sin(vφ))

And electric potential outside becomes:

V = a

_{o}+ b

_{o}ln(s) +Σs

^{-v}(c

_{v}cos(vφ) + d

_{v}sin(vφ))

There is also symmetry along the x-axis so we can ignore the sin(vφ) contribution:

V = a

_{o}+ b

_{o}ln(s) +Σ(s

^{v}(a

_{v}cos(vφ))

V = a

_{o}+ b

_{o}ln(s) +Σ(s

^{-v}(a

_{v}cos(vφ))

Do I need to solve for a

_{o}and b

_{o}? How would I use the boundary conditions?