I'm designing a comb drive and have read many papers that derive the force
produced by a comb drive as the following equation:

F=(Er)*(Eo)*(T)*(N)*(V^2) / 2g

where:  Er=relative permittivity; Eo=permittivity of free space; N =# of
fingers; T=thickness of electrodes; V=driving voltage; and g=separation gap.

The units however do not work out for this equation unless you multiply it by
coulomb's constant with units Nm^2/C^2.  Can someone let me know if I'm missing
something here since the results change by a factor of 10^9 depending on whether
or not it is used.  Thanks


Eric