Perhaps the easiest way to asnwer this is to think of radio waves which of course always follow a great circle path between points.
So ignoring range limitations and variation/deviation and with no wind effect think of the following.
VOR B is on the 300 radial at 3000nm when measured at VOR A
So the initial great circle track at VOR A is 300.
If the pilot follows the radial continuously, the no wind true heading (rhumb line track) will change becuse we are following a great circle.
If however, we maintain a constant heading (rhumbline track) of 300, one can easily picture how we will diverge from the VOR radial (depending on hemisphere).