Question

A positively charged particle is held at the center of a spherical shell. The figure gives the magnitude E of the electric field versus radial distance r. The scale of the vertical axis is set by E_s = 8.0

Answer 1

there are two discontinuities in the graph that are half a Centimeter apart.

There are no numerical values on the vertical scale. Assumptions need to be made about what the separation of the horizontal lines represents. It is not even beyond the realm of possibility that the bottom line represents a field strength of something other than zero.

Perhaps the Es=12.2*10^7 N/C is describing the effect of a voltage differential between the two surfaces of the shell. The graph has about 6 divisions between the field strength just inside the inner surface and just outside the outer surface. This would make the gaps between the horizontal lines to represent slightly more than 2*10^7 N/C.

Perhaps the Es in the upper left hand corner of the graph is supposed to be representing a field strength of 8*10^7 N/C. This would make the gaps between the horizontal lines to represent approximately 1.2*10^7 N/C.

Holding a charge at the center of a spherical shell is next to impossible. A small sphere with charge evenly spread over the surface would have almost identical effects as a point charge. Because of the wording of the problem, I was expecting a shell of infinitesimally small thickness. The excess charge on a real shell of almost any material should be on the outer surface of the material. Inside the material portion of the shell there should be no electrical field strength differential. If there were then there would be a current and eventually the differential would be eliminated. I therefore believe that the bottom line must represent zero field strength.

8*10^7/9/10^9/3*10*5*5/100/100=charge on outer edge of shell
or about 110?C