i) If “a” is directly proportional to “b”, this means that a = k x b, where k is a constant. If “a” is inversely proportional to “b”, this means that a = k x 1/b, where k is a constant.
Since we know that F is inversely proportional to the square of d, this means that the equation is:
F = k x 1/d2
F = k/d2
b) When d is halved, d becomes d/2,
so, F = k / (d/2)2
F = k/ (d2/4)
F = 4k/d2
From this, we can tell that when d is halved, the force of repulsion is quadrupled (x4).
Therefore, the force when d is halved is:
20 Newtons x 4 = 80 Newtons