(Solution) - Two spherical cavities of radii a and b are hollowed out -(2025 Original AI-Free Solution)

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Two spherical cavities, of radii a and b, are hollowed out from the interior of a (neutral) conducting sphere of radius R (Fig. 2.49). At the center of each cavity a point charge is placed???call these charges qa and qb.
(a) Find the surface charges ?a, ?b, and ?R.
(b) What is the field outside the conductor?
(c) What is the field within each cavity?
(d) What is the force on qa and qb?
(e) Which of these answers would change if a third charge, qc, were brought near the conductor?