Principle and Working:
Repulsive forces between two current carrying conductors, which is very small, is measured using a very sensitive balance technique based on a diode laser, scale and fractional weights to form an optical lever. This measurement is used to calculate permeability of air.
Similarly small attractive forces between two charged capacitor plates is measured. This measurement is used to calculate the permittivity of air.
An indirect estimate of the speed of light can be made from the experimental values of permeability and permittivity which verifies the relationship.