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Advanced Physics Homework Help
Calculating the electric potential
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[QUOTE="physicsisfun0, post: 6088239, member: 653683"] [h2]Homework Statement [/h2] [ATTACH=full]233972[/ATTACH] 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[SUB]o[/SUB]. The fourth section is grounded so electric potential is zero. We are looking for electric potential inside and outside of the pipe. [h2]Homework Equations[/h2] For electric potential I have: V = a[SUB]o[/SUB] + b[SUB]o[/SUB]ln(s) +Σ(s[SUP]v[/SUP](a[SUB]v[/SUB]cos(vφ) + b[SUB]o[/SUB]sin(vφ)) + s[SUP]-v[/SUP](c[SUB]v[/SUB]cos(vφ) + d[SUB]v[/SUB]sin(vφ)) We also know boundary conditions: [ATTACH=full]233973[/ATTACH] [h2]The Attempt at a Solution[/h2] (I think this next part is right) And electric potential inside becomes: V = a[SUB]o[/SUB] + b[SUB]o[/SUB]ln(s) +Σ(s[SUP]v[/SUP](a[SUB]v[/SUB]cos(vφ) + b[SUB]o[/SUB]sin(vφ)) And electric potential outside becomes: V = a[SUB]o[/SUB] + b[SUB]o[/SUB]ln(s) +Σs[SUP]-v[/SUP](c[SUB]v[/SUB]cos(vφ) + d[SUB]v[/SUB]sin(vφ)) There is also symmetry along the x-axis so we can ignore the sin(vφ) contribution: V = a[SUB]o[/SUB] + b[SUB]o[/SUB]ln(s) +Σ(s[SUP]v[/SUP](a[SUB]v[/SUB]cos(vφ)) V = a[SUB]o[/SUB] + b[SUB]o[/SUB]ln(s) +Σ(s[SUP]-v[/SUP](a[SUB]v[/SUB]cos(vφ)) Do I need to solve for a[SUB]o[/SUB] and b[SUB]o[/SUB]? How would I use the boundary conditions? [/QUOTE]
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Calculating the electric potential
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