Electric cars motors are powered by the batteries the batteries are typically Lead-Acid or Lithium Ion batteries. Batteries will normally stay charged in between 100-300 miles and take 3-8 hours to charge.
I think that the one of the things that electric cars should work in car shops is one of the external parts of an electric car like wheels or chassis. The engine of an electric car doesn't need to be...
No one invented a specific electric car battery, it was more a gradual thing starting with a generic battery and then step by step changing it to something more suited for the specific requirements...