# Maxwell’s Equations Reveal Ideal Location For Wi-Fi Router

Like so many of us, Jason Cole was fed up with the spotty internet in his apartment. A PhD student studying physics at Imperial College London, Cole used his mathematical expertise to determine the ideal location for his Wi-Fi router. Not only did Maxwell’s equations help solve his daily frustrations, but they have actually made him some money, because he has developed an app that allows people to perform simulations of their own homes.

He described the process in The Conversation. “The electromagnetic radiation emanating from the antenna in your wireless router is caused by a small current oscillating at 2.4GHz (2.4 billion times per second),” he wrote. “In my model I introduced a current like this and allowed it to oscillate, and Maxwell’s equations dictated how the resulting electromagnetic waves flow. By mapping in the actual locations of the walls in my flat, I was able to produce a map of the Wi-Fi signal strength which varied as I moved the virtual router.”

The results clearly showed that a router should ideally be positioned with a line-of-sight to where you will be using the internet. This conclusion was expected, since it is well known (in the scientific community, at least) that Wi-Fi signals are weakened when travel through walls. A more surprising conclusion was that even a slight change of the router’s position could greatly improve signal strength. The simulation mapped dark spots that represent standing waves, where two waves of identical frequency create interference that cancels the signal Wi-Fi signal altogether. Cole’s simulation helps identify the ideal places to put a router in order to move these dead zones. For example, you might reposition your router so that a Wi-Fi dark spot moves from your office to the bathroom.

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Cole originally created the simulation to solve his personal Wi-Fi troubles, but he later created an app so that people could simulate electromagnetic wave-based solutions for their own homes. The app uses the 2D Finite Difference Time Domain method to solve Maxwell’s equation on a Cartesian grid. Users upload an image of their floorplan to the app and add a few more details about antenna parameters and the material of the walls. Then the app runs a simulation that maps out theoretical Wi-Fi signals and shows the ideal location for the router. You can download the app for \$1 to try it yourself. Spoiler alert: it will likely be the center of your home.

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