Why is the strength of a field (i.e. gravitational or electric) inversely correlated to the square of the radius?
It is clear to me why the further you get a way from a field, the field's enacted force decreases. However, this makes me hypothesize that the relationship should be:
$$F ~=~ k/r$$
However, it is in fact:
$$F ~=~ k/r^2$$
Is this related to the fact that the surface area of a sphere is a function of the square of its radius?
An intuitive explanation would be very much appreciated.