  Many students meet quite early this dipole-dipole potential energy when they
are taught electrostatics or magnetostatics, and it is also a very popular
formula, featured in the encyclopedias. We show that by a simple rewriting of
the formula it becomes apparent that for example, by reorienting the two
dipoles, their attraction can become exactly twice as large. The physical facts
are naturally known, but the presented transformation seems to underline the
geometrical features in a rather unexpected way. The consequence of the
discussed features is the so called magic angle which appears in many
applications. The present discussion also contributes to an easier introduction
of this feature. We also discuss a possibility for designing educational toys
and try to suggest why this formula has not been written down frequently before
this work. Similar transformation is possible for the field of a single dipole,
there it seems to be observed earlier, but also in this case we could not find
any published detailed discussion.
