Philip P. answered 11/08/15
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The Coulomb Force is an inverse square force; that is, it's proportional to 1/r2 where r is the distance between the particles.
F = (1/4piε0)*q1q2/r2
so when you cut the distance in half, the force increases by a factor of four: 1/(1/2)2 = 1/(1/4) = 4.