(EM Griffiths) Problem 2.1 (d)

Question
If one of the 13 q's is removed, What is the force on Q?

Answer

Similar to the problem 2.1(b), the answer is
$F_Q = Qq/4\pi\epsilon_or^2$

Where r is the distance between charge Q and q.

Reasoning is easy. One missing charge breaks the symmetry of the problem. As a result of that charges sitting at corners other than the vacant site impose resultant coulomb force of amount $F_Q$ upon the test charge Q. We can easily prove it analytically (by using calculus).