physics problem?

Question

Find the potential due to a thin, uniformly non-conducting charged rod of length 2a at the point (y,z). Take the rod along the z axis

Answer 1

Take the rod along the z axis, and the middle point of the rod at the origin. Also let the charge density on the rod be p. We have:
P(r,z) = [integral](z: -a to a) pdz/sqrt(r^2+z^2)
= | p*ln(z+sqrt(r^2+z^2)) |(z: -a to a)
= p*ln(sqrt(r^2+a^2)+a) - p*ln(sqrt(r^2+a^2)-a)
= 2p*ln((sqrt(r^2+a^2)+a)/r)
where r is the radius from the z-axis, hence P(r,z) is the potential on a circle in the plane parallel to x-y plane and centered at (0,0,z). Note (x,y,z) is a point, rather than (y,z).