Mutual external inductance (MEI) associated with fringing magnetic fields in planar transmission lines is a cause of socalled "ground plane noise", which leads to radiation from printed circuit boards in high-speed electronic equipment. Herein, a Method of Edge Currents (MEC) is proposed for calculating the MEI associated with fringing magnetic fields that wrap the ground plane of a microstrip line. This method employs a quasi-magnetostatic approach and direct magnetic field integration, so the resultant MEI is frequency independent. It is shown that when infinitely wide ground planes are cut to form ground planes of finite width, the residual surface currents on the tails that are cut off may be redistributed on the edges of the ground planes of finite thickness, forming edge currents. These edge currents shrink to filament currents when the thickness of the ground plane becomes negligible. It is shown that the mutual external inductance is determined by the magnetic flux produced by these edge currents, while the contributions to the magnetic flux by the currents from the signal trace and the finite-size ground plane completely compensate each other. This approach has been applied to estimating the mutual inductance for symmetrical and asymmetrical microstrip lines.