In the Figure, a Conducting Sphere of Radius $r _ { 1 } = 0.050 \mathrm {~m}$

In the figure, a conducting sphere of radius $r _ { 1 } = 0.050 \mathrm {~m}$ is placed at the center of a spherical conducting shell of inner radius $r _ { 2 } = 0.100 \mathrm {~m}$ and outer radius $r _ { 3 } = 0.140 \mathrm {~m}$ . The inner sphere carries an excess charge of $- 4.0 \mathrm { nC }$ . The outer spherical shell carries a net excess charge of $3.0 \mathrm { nC }$ . Calculate the magnitude of the electric field at the following distances $r$ from the center of the spheres. $\left( k = 1 / 4 \pi \varepsilon _ { 0 } = 9.0 \times 10 ^ { 9 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { C } ^ { 2 } \right)$
(a) $r = 0.075 \mathrm {~m}$ (in the air space between spheres),
(b) $r = 0.120 \mathrm {~m}$ (in the metal of the spherical shell), and
(c) $r = 0.200 \mathrm {~m}$ (outside the spherical shell).