Overlapping Charged spheres: solve Electric Force of point charge (Q) locations

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I need help understanding how to calculate various Electric Field Strengths of several point charges (Q) both inside and along two OVERLAPPING identical spheres BUT with on NON-UNIFORM VOLUME CHARGE DENSITIES (-1p non-overlap density on the outside with -4p density overlapping internally) with both having identical radii (R). These spheres are identical expect for these volume charge densities.

I started with: E(sphere) = Q/4pi(Eo)R^2

1) Is E(total) as the sum of three vectors: E1, E2, E(overlap) and combine all three to calculate the net total (Etot)? OR: Is it just the two overlapping identical spheres minus (-) the overlapping common segment?

2) Is this the best formula for this scenario: Volume Density (ro: P) = Q/V(subscript little r)I=Q/(4/3)(pi)(r^2)?

Are there any "special" integration issues that must be evaluated first for that common overlapped segment that the two spheres share in common when solving for E(sphere)?

3) What are the trignomentric X, Y components of an abritary point charge Q that is placed along the edge of where these two overlapping spheres intersect with identical radius (r) at angle theta? The point Q is in between the two overlapping spheres at the 12 O-clock position in the respective X,Y plane Cartesian plane.

specifically, what is the easiest way to calculate strength of the Electric Field (E) at this common tangental point charge Q and its X,Y trigonmetric components (X hat, Y hat).

* assume 1st quadrant rules of TRIG are applied at this location for point charge: Q.

thank you for any advice...:-)
 

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