In the conventional partial element equivalent circuit (PEEC) method, all partial inductances are connected at both ends to other circuit elements of a PEEC or modified nodal approach (MNA), simulation program with integrated circuit emphasis (SPICE) type circuit. This article shows that if at least one end of a partial inductance remains without a connected element, it is called an open loop, which is also physical and is theoretically closed by displacement current. It is shown in this article that the open loop is only consistent if the partial inductance is evaluated using the Coulomb gauge; else, the magnetic energy computation of open loop is inconsistent. This article focuses on the difference and presents an analytical method for the calculation of partial inductance with Coulomb gauge in quasi-static field to figure it out. This difference is proven to be related to the calculation of vector potential <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</i> , whereas existing calculation is based on Lorentz gauge. Then, analytical results of conductor segments are derived for comparison of the two different gauges, and show the difference. Also, numerical experiments of the self- and mutual-partial inductances of conductor segments in open-loop problems are given for further comparison. The results illustrate that the proposed method is consistent with magnetic energy, and could be directly be applied to closed-loop problems without affecting the validity of the PEEC method. This method is believed to be an effective supplement in physical sense of partial inductance.