The spiral structure of the interplanetary magnetic field (IMF) is known to induce intramagnetospheric azimuthal magnetic field urn:x-wiley:jgra:media:jgra55432:jgra55432-math-0002, which strongly correlates with the IMF urn:x-wiley:jgra:media:jgra55432:jgra55432-math-0003. We reconstruct this effect for the first time in 3‐D, using a large set of data taken in the near/inner magnetosphere and a flexible magnetic field model based on expansions in radial basis functions (RBF). The RBF model serves here as a magnifying glass with tunable resolution, focused on the specific region of interest. In this study, we used it to explore the IMF‐induced urn:x-wiley:jgra:media:jgra55432:jgra55432-math-0004 both on a global scale (i.e., for the entire range of local times) and in the night sector only, to better visualize details in the region with the strongest “penetration” magnitude. The induced urn:x-wiley:jgra:media:jgra55432:jgra55432-math-0005 was found to maximize on the nightside at distances urn:x-wiley:jgra:media:jgra55432:jgra55432-math-000610–12 urn:x-wiley:jgra:media:jgra55432:jgra55432-math-0007, where it concentrates around the solar‐magnetic equator and bifurcates into a pair of peaks located in predawn and postdusk sectors. The urn:x-wiley:jgra:media:jgra55432:jgra55432-math-0008 “penetration” is associated with the IMF‐induced asymmetry of field‐aligned currents at the plasma sheet boundary. Even on a statistical level, the peak values of the induced urn:x-wiley:jgra:media:jgra55432:jgra55432-math-0009 can substantially exceed the external IMF urn:x-wiley:jgra:media:jgra55432:jgra55432-math-0010. The effect is significantly stronger under southward IMF urn:x-wiley:jgra:media:jgra55432:jgra55432-math-0011 conditions and grows with increasing geodipole tilt angle.