A hollow non-conducting spherical shell has inner radius R_{1} = 5 cm and outer radius R_{2} = 13 cm. A charge Q = -35 nC lies at the center of the shell. The shell carries a spherically symmetric charge density ρρ = Ar for R_{1} < r < R_{2} that increases linearly with radius, where A = 23 μC/m^{4}.

a.) Write an equation for the radial electric field in the region r < R_{1} in terms of Q, r, and Coulomb’s constant k. (take the positive direction outward.)

b.) What is the radial electric field at the point r = 0.5R_{1}? (take the positive direction outwards.)

c.) What is the radial electric field at the point r = 0.5 (R_{1}+R_{2})?

d.) What is the radial electric field at the point r = 2R_{2}?