If currency exists in a solenoid, we can know the polarity.
However, there is no currency in DNA.how to define its polarity then?
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When people discuss the 'charge' of DNA being negative they are referring to the charge within the molecule.
The Phosphates (big red red and blue in the space filling diagram) have a negative charge and make the DNA both water soluble and negatively charged.
One can also talk about the 'directionality' of DNA which simply means that all DNA is 'read' and synthesized in the 5' to 3' direction (referring to the sugar backbone carbon). That's simply how all enzymes make DNA and RNA molecules and how we define the direction of the DNA code.
As far as I know there is no current running through the DNA itself and no pole in that sense.