Electrostatic Force between 2 charged bodies

A thin spherical non-conducting sphere of radiua R carries uniform surface charge density ($sigma $ ).It is cut into two parts by a plane at a distance R/√2 from center as shown. To hold two parts together force F has to be applied. Find force F ? (assume charge dosen’t redistribute after cutting)

The answer provided by my textbook uses the concept of electrostatic pressure to find force on one part(electeostatic pressure at any point on sphere is $ sigma^2 $/2$ epsilon° $). But the electrostatic pressure at any point is due to whole sphere and we have to calculate force on part 1 only due to part 2(we have considered force due to elements of part 1 on itself also). Is my textbook correct ? If not can anyone suggest any other way to solve it?