I apologize if this is the wrong way to post this. I'm new to this forum.
If anybody else has been tearing their hair out trying to figure out how to change the ownership of an external hard drive from 'root' to 'user,' here's what I did:
Mount your external hard drive. Open the Disk Utility, and right click on the drive you wish to select for ownership change. You will see a 'Contents' line at the bottom of the screen, which includes the information 'Mounted at.' This will give you the directory pathway you'll need to change ownership. IMPORTANT: this pathway MAY or MAY NOT include /media/yourusername. Copy the pathway. Open terminal. At the command prompt, type: sudo chown -v user:user / paste the pathway you copied from Disk Utility's 'contents' line.
For me, this looked like: sudo chown -v linda:linda /mnt/ata-WDC_WD2500JB-00REA0_WD-WMANK5969909-part1 (for my first external hard drive)
sudo chown -v linda:linda /media/linda/0fa28325-9261-4731-9673-11be12208bf2 (for my second external hard drive).
I'm a humble newbie, not a programmer, but if these solutions work for you, great! Maybe a smart programmer will invent a tool to make it easier for us beginners to change ownership/grant permissions (hint, hint).