My problem is that I'm confused about a hint I was given in this problem. I usually use the law of cosine to find the length of [itex]\vec{r}-\vec{r'}[/itex]. But the hint here says that I should make it [itex][r^2 + (z - z_0)^2]^{1/2}[/itex] Where does this come from? I can't quite get my head around the geometrical idea of this hint. Can't the law of cosine be used here?
It's really hard to answer these questions when you don't specify what any of the terms mean, so I can only guess at what r-r' even is. It looks like a Pythagoras approach to give you the hypotenuse of the triangle with sides r and z-z0. How would you use the law of cosine, and what problem would using it solve?
I don't know how the hint is specifically formulated but I think the best way here is to use cylindrical coordinates. It may be that r' is the cylindrical radius of the charge element. The point P has r=0 and z=zo.