An analytic model has been developed to quantify the effects of magnetic field diffusion on plasmas accelerated by magneticJ×Bforces. We examine the penetration of equilibrium and perturbed magnetic fields into a conducting plasma. Analytic solutions are found for both fields for a power law time dependence of the equilibrium field at the field plasma interface. Results show that wavelengths longer than the magnetic field diffusion length penetrate the plasma shell faster than the equilibrium field. For wavelengths shorter than the magnetic diffusion length the perturbed field remains confined to the original field plasma interface and falls off rapidly inside the plasma. Application to imploding linear plasmas show good agreement with detailed two‐dimensional magnetohydrodynamic simulations.