So this is a two part problem, I did the first half and I\'m needing some help g

Question

So this is a two part problem, I did the first half and I'm needing some help getting started on the second, not entirely sure how to approach it. Can anyone give me a direction to head in? "Derive an expression for the electric field at a distance r from the center of a sphere of radius R that carries a uniform volume charge density Rho. Find the electric field at the center, a point halfway to the edge, and a point at the edge (A, B, and C, respectively as shown in the figure). Now consider scooping out a spherical cavity of radius R/2 as shown. Argue that this is equivalent to adding a sphere with radius R/2 that has a negative charge density -Rho. FInd the electric field at the same three points."

Explanation / Answer

1) E=rho*r/3epsilon0

at A E=0

at B E=rho R/6epison0

at c E=rho R/3epison0

2) at A E=+rhoR/6epsilon0

at B E=+rho R/6epsilon0

at C E=rho R/eepsilon0-rhoR/6epsilon0=+rho R/6epsilon0

inside the cavity the E is constant and is equal torho R/6epsilon0

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