In the figure shown sphere `S_(1),S_(2)` and `S_(3)` have radii `R,(R)/(2)and (R)/(4)` respectively `C_(1),C_(2)` and `C_(3)` are centers of the three spheres lying in a plane Angle `angleC_(1)C_(2)C_(3)` is right angle. Sphere `S_(3)` has a uniformly spread volume charge density `4rho.` the remaining pat of `S_(2)` has uniform charge density of `2rho` and the left over part of `S_(1)` has a uniform charge density of `rho`.
(a) Find electric field at a point A at a distance `(R)/(8)` from `C_(3)` on the line, `C_(2)C_(3)` (see figure)
(b). Find electric field at point B at a distance `(R)/(4)` from `C_(2)` on the line `C_(3)C_(2)` (See figure)

Answer

(a). `(sqrt(5))/(6)(rhoR)/(epsilon_(0))`
(b). `(sqrt(41))/(24)(rhoR)/(epsilon_(0))`