Electrical Machines based on Electric Fields
There are electrostatic motors. They can be a better choice than magnetic motors for some situations. 

For example, check out this electrostatic motor that can be using in places with very strong magnetic fields like near MRI machines...

http://www.shinsei-motor.com/English/techno/

Electrostatic motors can also very efficiently directly use high voltage at very low current. The one described here can run forever off the voltage differential between two wires separated by a few dozen feet of height...

http://www.rexresearch.com/elstatix/esgenmot.htm#sciam

Here is a practical book with lots of electrostatic motor information, including many designs can build yourself...

https://www.amazon.com/Electrostatics-Exploring-Controlling-Electricity-Includes/dp/1885540043/ref=as_sl_pc_ss_til?tag=joshcom-20&amp;linkCode=w01&amp;linkId=GY4GGJ3S5CKUMRHM&amp;creativeASIN=1885540043