  Classical 1/4 BPS configurations consist of 1/2 BPS dyons which are
positioned by competing static forces from electromagnetic and Higgs sectors.
These forces do not follow the simple inverse square law, but can be encoded in
some low energy effective potential between fundamental monopoles of distinct
types. In this paper, we find this potential, by comparing the exact 1/4 BPS
bound from a Yang-Mills field theory with its counterpart derived from low
energy effective dynamics of monopoles. Our method is generalized to arbitrary
gauge groups and to arbitrary BPS monopole/dyon configurations. The resulting
effective action for 1/4 BPS states is written explicitly, and shown to be
determined entirely by the geometry of multi-monopole moduli spaces. We also
explore its natural supersymmetric extension.
