The impedance per unit length is considered in situations where rectangular conductors are in close proximity (the geometry considered is that of a narrow slot with depth). Application of the previously derived right angle corner constant, when the conductors are far apart compared to the electrical scales of length (such as skin depth), is modified to account for proximity effects. Alternatively, when the conductors are close together compared to the electrical scales of length, the gap region is eliminated and the fields are induced by appropriate fictitious sources at the gap location. The local impedance per unit length is thus determined and various limiting cases of the conductor thickness (or depth) are considered. A comparison with the thin shell impedance approximation is also made.