Electric current of I amperes flows along the z-axis from (0, 0,-∞) to (0, 0, -a) and from there it spreads over a conducting sphere r = a in the -aθ direction, comes to the point (0; 0; a) and goes to (0, 0, ∞) again along the z-axis. What is the surface current density at a general point on the sphere where z = h?
surface current density = Js = Δi / Δl ; l = length , i = current
The Attempt at a Solution
I am pretty lost with this one. If I use the above equation for surface current density it seems like I need to do this
∫ i / L dl = ∫ i / z dz from z = -a to a
I know this isn't the answer. Its to simple and my professor would never assign something as simple as this. I think I have some conceptual issues and I fear that my relevant equation is incorrect. I had to miss lecture due to a trip to the ER and I am relying on a friends notes, nice guy but less than exemplary student.