On the properties of two-dimensional dipoles and magnetized bodies

Several little-known relationships between the two-dimensional magnetic dipole and its external field are discussed in both the spatial and spatial frequency domains. Extensions of the theory to arbitrary magnetization patterns are made, which lead to the familiar Wallace results as a special case. The magnetization conditions yielding one-sided flux patterns are analyzed. Several of the results are expressed in matrix notation, facilitating brevity. Finally some limitations on determining internal magnetization patterns from measurements of the external field alone are discussed.