On 10 January 1997 an isolated solar wind density pulse, with other interplanetary parameters remaining steady, led to an enhanced transpolar potential (ΦTP) that is not predicted by either the Weimer or Siscoe-Hill models. However, a magnetohydrodynamic simulation of the magnetosphere's response to a sudden increase in solar wind density does predict an ΦTP increase consistent with satellite observations during the 10 January 1997 event. The response is transient, decaying after several tens of minutes toward an equilibrium that is close to the original potential. The simulated ΦTP increase derives from erosion of the dayside magnetopause and transport of newly opened flux across the polar cap. The exponential decay of ΦTP results from inductance in the magnetosphere-ionosphere circuit.