- #1
mjordan2nd
- 177
- 1
Homework Statement
Consider a cylinder, radius R and length L. Suppose the cylinder is charged with a volume charge given by P+P0 + Bz, where p0 and B are constants. Find the force on a charge Q at the center of the cylinder.
Homework Equations
E=q/4*pi*e*r^2
The Attempt at a Solution
I first found the electric field contribution of a disk with uniform charge density on a point z above the center of the disk, where e is epsilon-not and o is the charge density on the disk.
[tex]\int \frac{z r o 2 \pi }{4 \pi e \left(r^2+z^2\right)^{3/2}} \, dr[/tex]
The indefinite integral gave me
[tex]-\frac{o z}{2 e \sqrt{r^2+z^2}}[/tex]
Evaluating from 0 to R gave me
(oz/2e)*(1/z-(z^2+r^2)^-1)
I then used this to evaluate the integral from -z/2 to z/2 on the cylinder, and came up with this expression:
[tex]\int_{-\frac{L}{2}}^{\frac{L}{2}} \left(\left(\frac{L}{2}+z\right) b+p\right) z \left(\frac{1}{z}-\frac{1}{\sqrt{r^2+z^2}}\right) \, dz[/tex]
I have two questions:
Have I gone about this problem correctly so far, and how do I proceed from here. I don't know how to evaluate the integral. I figured I'd calculate the E-field first and then the force.
Thanks for any help...