At low voltages, the rate of migration of the DNA is proportional to the voltage applied, i.e. the higher the voltage, the faster the DNA moves.   However, in increasing electric field strength, the mobility of high-molecular-weight DNA fragments increases differentially, and the effective range of separation decreases and resolution therefore is lower at high voltage. For optimal resolution of DNA greater than 2kb in size in standard gel electrophoresis, 5 to 8 V/cm is recommended.  Voltage is also limited by the fact that it heats the gel and may cause the gel to melt if a gel is run at high voltage for a prolonged period, particularly for low-melting point agarose gel.
The mobility of DNA however may change in an unsteady field.  In a field that is periodically reversed, the mobility of DNA of a particular size may drop significantly at a particular cycling frequency.  This phenomenon can result in band inversion whereby larger DNA fragments move faster than smaller ones in PFGE.