The induced deformation due to the pressure forces can be obtained by solving Navier's equation for linear elasticity at steady state, which is given by
To solve Navier's equation, the pressure forces must be obtained first; so the first step is to calculate the electric field composing the pressure forces.
Solution of Navier's Equation. Due to the absence of the body force, Navier's equation can be written as follows:
After substitution of [GAMMA] in (11), the solution to Navier's equation in spherical coordinates can be written as follows:
Navier's equation is solved at the equator (d is n/2); thus, the calculated [u.sub.r] is the same change dr in the optical path of the circumnavigating light:
Using Navier's equation, an optical WGM based electric field sensor can be constructed.