We use the am, an, as and the aσ geomagnetic indices to the explore a previously overlooked factor in magnetospheric electrodynamics, namely the inductive effect of diurnal motions of the Earth's magnetic poles toward and away from the Sun caused by Earth's rotation. Because the offset of the (eccentric dipole) geomagnetic pole from the rotational axis is roughly twice as large in the southern hemisphere compared to the northern, the effects there are predicted to be roughly twice the amplitude of those in the northern hemisphere. Hemispheric differences have previously been discussed in terms of polar ionospheric conductivities generated by solar photoionization, effects which we allow for by looking at the dipole tilt effect on the time-of-year variations of the indices. The electric field induced in a geocentric frame is shown to also be a significant factor and gives a modulation of the voltage applied by the solar wind flow in the southern hemisphere that is typically a ±30% diurnal modulation for disturbed intervals rising to ±76% in quiet times. For the northern hemisphere these are 15% and 38% modulations. Motion away from/towards the Sun reduces/enhances the directly-driven ionospheric voltages and reduces/enhances the magnetic energy stored in the tail and we estimate that approximately 10% of the effect appears in directly driven ionospheric voltages and 90% in changes of the rate of energy storage or release in the near-Earth tail. The hemispheric asymmetry in the geomagnetic pole offsets from the rotational axis is shown to be the dominant factor in driving Universal Time (UT) variations and hemispheric differences in geomagnetic activity. Combined with the effect of solar wind dynamic pressure and dipole tilt on the pressure balance in the near-Earth tail, the effect provides an excellent explanation of how the observed Russell-McPherron pattern with time-of-year F and UT in the driving power input into the magnetosphere is converted into the equinoctial F-UT pattern in average geomagnetic activity (after correction is made for dipole tilt effects on ionospheric conductivity), added to a pronounced UT variation with minimum at 02-10 UT. In addition, we show that the predicted and observed UT variations in average geomagnetic activity has implications for the occurrence of the largest events that also show the nett UT variation.