A hollow non-conducting spherical shell has inner radius R1 = 5 cm and outer radius R2 = 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 R1 < r < R2 that increases linearly with radius, where A = 23 μC/m4.
a.) Write an equation for the radial electric field in the region r < R1 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 = 0.5R1? (take the positive direction outwards.)
c.) What is the radial electric field at the point r = 0.5 (R1+R2)?
d.) What is the radial electric field at the point r = 2R2?