The bursts of relativistic electrons detected on Pioneer 10 upstream from Jupiter and within 400rj of the planet have been found to be correlated with the interplanetary magnetic field. In the three examples upon which this study is based, during the month prior to the Pioneer 10 encounter, electrons with energies between 3 and 6 MeV escaping from Jupiter's magnetosphere were observed only when the interplanetary magnetic field was along the Jupiter-spacecraft line. In addition, large-amplitude interplanetary waves with characteristic periods of 10 min were observed and found to be well correlated with intervals during which the field was along the Jupiter-spacecraft line. Abrupt changes in the field away from the preferred direction caused equally abrupt terminations of the waves with an accompanying reduction in the electron flux. These results are consistent with propagation of the electrons from Jupiter to Pioneer along, rather than across, the magnetic field lines. The direction of the interplanetary magnetic field is apparently not affected by the electron bursts or by other particles from Jupiter. A histogram of 1-min averages of the interplanetary magnetic field longitude during the period of the study clearly shows the average Parker spiral direction with no enhancement in the Jupiter-spacecraft direction. Two alternative possibilities are considered for the origin of the waves. If they were generated near Jupiter, they would have to propagate to the spacecraft in the whistler mode. The expected attenuation of these waves over distances of several hundred rj an their long travel times make this explanation unattractive. Alternatively, hydromagnetic wave generation by Jovian charged particles, presumably the relativistic elecltrons themselves, as they travel upstream, appears to be an attractive explanation. At the observed frequency, hydromagnetic waves are Doppler-shifted to the gyrofrequency of the relativistic electrons. A plasma instability that appears capable of explaining the observations is a cyclotron overstability originally discovered in thermonuclear research that occurs when the velocity of runaway electrons exceeds the velocity of hydromagnetic waves.