Ring of charge (half positive, half negative)

[jtran06]

Homework Statement

Two half-rings of charge of opposite polarity are brought together at the origin (so that the rings create a full circle against the y- and z-axis. Each half-ring has a charge of magnitude Q and radius a. Derive the net electric field at point P, located on the +x axis a distance d from the centre of the two half-rings.

Homework Equations

Not sure.

The Attempt at a Solution

I really have no idea how to work this out from what we learned in lecture; "electric field of a ring of charge".. Help, please!

 

[haruspex]

As start, can you figure out the direction of the field there? Let the line of join of the semicircles be the y-axis, say. Consider separately the components of the field in the x, y and z directions. Can you see any that must cancel by symmetry?

 

[jtran06]

I've worked it out conceptually to see that only those in the z direction do not cancel out but I'm at lost on how to retrieve that mathematically.

 

[vela]

Explain to us how to find the field due to a ring of charge then — you know, what you went over in lecture. If you understand what was done there, you should be able to make a dent in this problem.