A conducting, thick spherical shell of inner radius \(100 \mathrm{~mm}\) and outer radius \(120 \mathrm{~mm}\) has no net charge. A particle carrying a \(3.0-\mathrm{nC}\) charge is placed at its center.

(a) Draw the electric field line diagram for the situation, marking the location of all charge on your diagram.

(b) Calculate the surface charge density at the inner and outer shell surfaces.

(c) Determine the electric field as a function of \(r\), the radial distance from the center of the shell.

(d) Draw an electric field line diagram for the situation when the particle is displaced by \(30 \mathrm{~mm}\) from the shell's center.