Recently, I have learnt about the central force motion. I came across some forces with different distance dependence, for example, k/r^2(common) one, k/r^4, or even the combined one k/r^2 + k'/r^4 (k, k' are force constant).
I remembered when I first learnt the inverse square law, I was convinced that the inverse square law came from the density of the field line on a surface. However, how the forces with 1/r^3, 1/r^4 exists? Can they be derived by classical means?
I have searched for different information but I cannot get a good answer. I hope someone can help me, or relevant reference will do.