Question

On PSet 8, on problem 4A, #4 (the one with the current carrying wire along the Z-axis), how are they getting their answer? I've done problems exactly like this in physics, and if r=(x^2 +y^2)^1/2, then the field at any given point should be /r^3 , or /(x^2 +y^2)^3/2 What's going on?

Answer 1

They give all the background (the physics is correct, see http://faculty.wwu.edu/vawter/PhysicsNet/Topics/ElectricForce/LineChargeDer.html)
and they want you to write down a field that points in the correct direction and has the correct magnitude at every (x,y) point in space.

with the wire oriented along the z-axis, consider the field in the x-y plane at z=0
draw a radius from the wire to the arbitrary point (x,y)
this radius has length \( \sqrt{x^2+y^2}= r \)
the field is perpendicular to the radius, lies in the x-y plane , and points ccw
i.e. <-y,x>
normalize to unit length: <-y,x>/r
now scale by the strength of the field, given by k/r
you get
\[ k \frac{<-y, x>}{r^2} \]

Answer 2

Crap, you're right, I forgot to integrate XD!