This video goes through the steps on how to move your ownCloud data to a new location.
The steps used in the video are below:
Stop apache2
sudo service apache2 stop
Edit config file in default location
sudo nano /var/www/html/owncloud/config/config.php
Change default location to new location
(please check video)
Move the data folder to new location
sudo mv /var/www/html/owncloud/data /mnt/owncloud_data
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if required change permissions
sudo chown -R www-data:www-data /mnt/owncloud_data
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Restart apache2
sudo service apache2 start