Check out the laws of thermodynamics,
energy can not be created,or destroyed.
only converted.
Perpetual motion is a myth.
As current understanding goes.
What your suggesting is creation of more energy than you started with.
Not going to happen.
Even the energy in an electric vehicles power cells was converted from another source at the power station.
Coal,gas,atomic..............
If you trace all source back they all come from one source,
the sun,
Even Hydro electric would not exist without solar energy driving the weather and rain fall.
Much the same as when internal combustion started the problem is energy storage,
When the first cars were sold there were no fuel stations,
anywhere!
But liquid fuel dumps were easy to set up.
There were electric vehicles back then too,
but electricity has to be generated and then run down wires.
And then,just like now it all comes back to money,everything eventually does.
It was a lot cheaper,and faster to set up for internal combustion supply systems.
Going back to your electric car problem,it's not really a problem of re charging so much as a storage problem.
Battery systems need to be developed to store much more.
Something like 24 H charge and 1000K range will come.
Of course then the tax man will take a lot of interest!!
A good electric car has regenerative braking, which does act a bit like a dynamo, charging the battery when the car is braking.
Otherwise, you need an engine to provide energy to drive the dynamo - resulting in a hybrid.
Solar cells on the roof would help a little, too, providing some recharging off the net.
You can't get something for nothing - driving the dynamo would drain even more power from the battery than it would provide - you can't get even 100% efficiency, let alone more than 100%, which is what you are suggesting.
Okay, I suppose I was thinking of the days when you could fit a dynamo to your bicycle to help power your lights as you peddled, obviously not as simple as it sounds. I might as well buy a petrol car, then.....
They've done that, it's called a hybrid car.
Concerning electric cars and their limited range, (you either allow enough time and energy to get home in time to charge it again or find an outlet at your destination), why can`t the system have a dynamo fitted to help charge the battery as well as help power the system on the move, or am I verging on the theory of Perpetual Motion, which still seems to be the work of Sci Fi writers?