Backing up on a second computer

jeol1029, if what I am understanding correctly what you're describing: your iPad has been synced with Computer 1 (at work) and you are now trying to make a copy of your iPad onto Computer 2 (at home). I had a similar situation, and what I did was:

1. From the Store menu, authorize iTunes on Home Computer with the same account used to acquire the apps on the iPad.

2. Connect iPad to iTunes.

3. Under the File option, select "Transfer Purchases from (device name)".

As you've surmised, clicking on "Sync" will effectively replace your iPad with whatever is in your iTunes library, and if there are no apps there, iTunes will sync "nothing" to your device, effectively cleaning it out.

The Apple support page for this (with a bit more detail) is at: iTunes Store: Transferring purchases from your iPhone, iPad, or iPod to a computer