When the solar wind interacts with the moon, the plasma shadow region on the dark side of the moon forms a long lunar wake. In the plasma umbra a detectable plasma flow is absent and in the penumbra the plasma flux increases from the void condition in the umbra to the interplanetary condition outside. A theoretical model for perturbations of the magnetic field in the plasma shadow is studied by directly solving Maxwell's equations for steady‐state solutions. The perturbation of the field is assumed to be due to the magnetization current, the gradient drift current, and the curvature drift current. Numerical solutions are obtained to describe the variations of the magnetic field, and the results are in good agreement with experimental observations from the Explorer 35 satellite.