- #1
RJLiberator
Gold Member
- 1,095
- 63
Homework Statement
A disc of radius R lying in the xy-plane is composed of an inner disc of radius R/2 carrying a uniform surface charge density +σ and an anulus (inner and outer radii of R/2 and R) carrying a uniform surface charge density -σ. Assume that the inner disc and the annulus are electrically insulated from each other by an insulating strip of neglibible thickness placed at their intersection at R/2.
a) Calculate the potential V at the point (0,0,z) along the z-axis using infinity as the reference point. Show by making a Taylor expansion i n1/z that z dependence of your answer makes sense in the z->∞ limit.
Homework Equations
##V = \frac{1}{4 \pi ε_0} \int \frac{σ}{r} dτ##
3. The Attempt at a Solution
So this is a multi-part problem and I can get parts b,c, and d if I can figure this potential out.
When I try I get this:
[tex]V(0,0,z) = \frac{1}{4 \pi ε_0}\int_0^z \frac{σ}{z} dz [/tex]
Which evaluates to ##V(0,0,z)=\frac{1}{4 \pi ε_0}\frac{σ}{z^2}##
But this doesn't make sense to me. I mean, I have the differences in charge densities to consider, and so on. So I ask for hints on what I am doing wrong here and how I can understand how to use this equation better. Am I not understanding what r is suppose to be in this case? How can I consider the -σ and +σ.