Your charger will work, to an extent. If your power usage is high - bright screen, lots of activity, etc, it will only be able to slow the discharge, not keep it charged indefinitely. However if you close the Macbook and let it charge, it will charge - although still slowly. The 12w adapters that were included for a couple of years are slightly better still than the 10w charger you have. I keep my Macbook topped off at home in the kitchen from one of these and it generally works ok.