Force on point charge caused by another point charge.

[woprxcpe1704tks]

Homework Statement

Consider two equal point charges q, separated by a distance 2a. Construct the plane equidistant from the two charges. By integrating Maxwell’s stress tensor over this plane, determine the force of one charge on the other.

I have the full solution, but I'm confused on one part. Where does the E=1/4pi...cos(θ)r come from? And by that I mean where does each component come from? I know about the 1/4piε0, but I don't understand the rest.

Full Solution

 

[mfb]

Where does the E=1/4pi...cos(θ)r come from?

Apart from the cosine, it is the standard electrical field strength from a point charge. The cosine then evaluates the component perpendicular to the plane.

And by that I mean where does each component come from?

That follows from geometry.

 

[TSny]

There's a bit of confusion with the diagram which shows opposite signs for the charges, yet the vectors showing the individual fields are for two positive charges. The problem statement and the solution are for charges of the same sign.

Will the net field be parallel to the xy plane or perpendicular to the plane?