At the top of the 'Car Questions' home page, on the right side you will see a 'search' bar. Type in "EV self charging" and you will find a thread (the forth from the top) entitled, "Answer to EV constant charging possible". The response by @Dan which is almost at the end of the thread (second from the bottom) is a great tutorial on this subject.

Because then we could all install such a system in our homes and get free power forever.

You have got to be trolling.

They won't because it's an impossibility. You're describing a perpetual motion machine, which violates several physics laws. 

When you're driving (maintaining constant speed), the battery is discharging. You can never get the energy back out. You can recharge the battery when you're slowing down, since that energy will otherwise be converted into heat via the brake pads. 

Basically, in order to charge a battery in a vehicle, you need an energy source external to the car. The power coming out of the wall or charging station came from a power plant, which came from its generator. The generator was turned by steam that was generated by a heat source -natural gas, coal... 

Posted by: @govenor

I was wondering why the electric car companies don't design and install a charging system that will recharge the batteries while the cars is cruising down the interstate highway.

Think back to grade-school science class.

Conservation laws including: conservation of mass and energy, conservation of linear momentum, conservation of angular momentum, and conservation of electric charge.

https://www.youtube.com/watch?v=Np1Ixd7FWzI

Scotty answers the question @ 7:46

https://youtu.be/whpAHGH9NFo?t=466

I think the moral of the story is that you'll never outsmart engineers by skipping the research.