• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Potential of all space from sphere

  • Thread starter Datadep5
  • Start date
1. Homework Statement
Consider a sphere or radius a. The top hemisphere has a uniform charge density [tex]\sigma[/tex], the bottom has -[tex]\rho[/tex]. Calculate the electric potential in all space.[tex]\sigma[/tex]


2. Homework Equations
Laplace's Equation:
[tex]\nabla[/tex][tex]^{2}[/tex]=-4[tex]\pi\sigma[/tex]

Potential (solved from Laplace's Equation):
V=[tex]\int\frac{\rho(r)}{r}[/tex]d[tex]\tau[/tex]


3. The Attempt at a Solution
I solved laplace's equation to get the potential is the integral over rho/r. I want to integrate from 0 to a, and then a to R; where R is some arbitrary point. I want to just plug in [txt]\sigma[txt] times a, for the charge, and integrate it over r.

I'm not sure how to treat the -[txt]\sigma[txt]. Any ideas?
 

Want to reply to this thread?

"Potential of all space from sphere" You must log in or register to reply here.

Related Threads for: Potential of all space from sphere

Replies
5
Views
1K
  • Posted
Replies
12
Views
1K
  • Posted
Replies
2
Views
2K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top