IOS – Whats the value for DNS when you leave blank DNS in static IP

What you want to do is Add a Network Location for work.

You can then easily switch between them using the Location submenu of the  menu.

If you really wanted, you could set up a script to switch locations based on network, but really, how lazy do you want to be? ;)

What you're describing is a split-horizion DNS setup.

There's a pretty good walkthrough on how to do exactly what you want to do, but it will require root on your laptop and some command line patience to setup. In a nutshell, you'll be configuring your own DNS server on the laptop to forward your DNS requests to the right server.

If you're on Mavericks (not sure yet about Yosemite), it looks like bind isn't installed anymore. You'll want to get it with homebrew or similar. Check out this stack overflow Q/A. It should also have a default named.conf that you can just edit, but YMMV.