It doesn't say anything about polarization of the external power in
the manual or on the board. Is it minus inside/plus outside or plus
inside/minus outside?
"7.3 Connecting Optional Power
An optional DC supply can be used to power the BeagleBoard by plugging
it into the power jack of the BeagleBoard. The power supply is not
provided with the BeagleBoard, but can be obtained from various
sources. You need to make sure the supply is a regulated 5V supply.
Figure 7 shows where to insert the power supply into the power jack.
Figure 7. DC Power Connection
The power supply must have a 2.1mm I.D x 5.5mm O.D. x 9.5mm and can be
either straight or right angle. Connecting anything other than 5V will
result in damage to the board. If you are using the USB OTG port in
the OTG or host mode, you must have an external DC supply powering the
BeagleBoard."
Roddi