Step 6: Cut Rod to Fit
The aluminum rod will be the contact that presses against the post in the middle of the socket on the laptop. It's tricky to get the length perfect, so you'll want to spring-load it. The spring-loaded rod sticks out further than it needs to, but then the pull of the magnets compresses the spring and the rod and magnets both make firm electrical contact.
If you have a spring that fits perfectly in the hole already, then you can skip this paragraph. I couldn't find a small enough spring, so I modified a spring from inside a pen. Snip a short segment of spring from the pen, and then use a pair of needle-nose pliers to tighten the loops. Keep tightening and fixing until the spring is small enough to comfortably fit down the hole in the plug. Don't force it -- you never know when you'll want to take it out again.
Now you want to adjust the length of your aluminum rod so that, sprung, it is slightly too long. Put the rod in the chuck of your power drill and run it against some sandpaper to wear it down quickly. Start with coarse sandpaper, and finish off with fine to ensure a nice finish. Go through a bunch of iterations to make sure it's perfect. Go through some rounds of testing -- when you attach the plug to socket, does the rod get pushed back against the spring? Do the magnets still hold them together?
Once the rod is the right length, wrap a strip of scotch tape around the part that sticks out, so that only the tip is exposed. This will help prevent you from touching the powered-up rod to the ground washer on the laptop. You can put as many layers on as you want, as long as you don't exceed the size of the hole in the laptop.