Geometrical simplification of the dipole-dipole interaction formula

摘要

Many students meet dipole-dipole potential energy quite early on when they are taught electrostatics or magnetostatics and it is also a very popular formula, featured in 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 transformation presented seems to underline the geometrical features in a rather unexpected way. The consequence of the features discussed is the so-called magic angle which appears in many applications. The present discussion contributes to an easier introduction of this feature. We also discuss the possibility of designing educational toys and try to suggest why this formula has not been written down frequently before this work. A similar transformation is also possible for the field of a single dipole. In this case we found one such formula on the Web, but we could not find any published detailed discussion for this case either.