Two Concentric Spheres Are Shown in the Figure

Essay

Two concentric spheres are shown in the figure. The inner sphere is a solid nonconductor and carries a charge of +5.00 µC uniformly distributed over its outer surface. The outer sphere is a conducting shell that carries a net charge of -8.00 µC. No other charges are present. The radii shown in the figure have the values R₁ = 10.0 cm, R₂ = 20.0 cm, and R₃ = 30.0 cm. (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²)
(a) Find the total excess charge on the inner and outer surfaces of the conducting sphere.
(b) Find the magnitude and direction of the electric field at the following distances r from the center of the inner sphere: (i) r = 9.5 cm, (ii) r = 15.0 cm, (iii) r = 27.0 cm, (iv) r = 35.0 cm.