Thanks @vanhees71 for the explanation and @TSny for the clarification.
Indeed, if we take the final formula where ##E_r \propto r##, we get ## \frac{F(R/2)}{F(R)} = \frac{1}{2}##, the same result as Coulomb's Law for the equivalent point charge.
@vanhees71 , are you suggesting that more computation is needed and the answer for (1), constant charge density, is not ## \frac{F(R/2)}{F(r)} = \frac{1}{2}## as outlined above?
I've bought the book as new earlier this year and the pages look white, so it must have been printed quite recently. There's no info about a specific printing, the copyright section mentions 1960, 1962, ..., 1992, 2002.
Looking at the preface, it mentions that computing the force for a line of...
This is SAMPLE PROBLEM 25-7 from "Physics" by Resnik, Halliday, and Krane, in the chapter "Electric Field and Coulomb's Law".
After describing the behavior of uniformly charged spherical shells:
follows a sample problem:
The solution to (a) goes to say that the volume inside R/2 is 1/8 of the...