The theory of Rayleigh-B'{e}nard convection of a horizontal liquid layer with upper free surface over a heated plate has many important applicatios in a number of engineering problem such as extraction of oil from porous medium etc. The gravitational field on the earth is not constant. It is always fluctuating, this fluctuating gravitational field is called as g-jitter or Gravity modulation.

So, convecion under the fluctuating gravitational field is a main class of problems which helps us to study convection problem in a microgravity condition. Variation of the gravitational field affects the stability of the system even though basic temperature gradient is identical. The effect of Gravity modulation on a stable convection configuration can affect the stability of the system under consideration may be by increasing or decreasing the rate of convection. In general, a distribution of stratifying agency that is convectively stable under constant gravity conditions can be destabilized when a time-dependent component of the gravity field is introduced certain combinations of thermal gradients, physical properties and modulation parameters may lead to parametric resonance and hence, to the stability of the system. Bhadauria and Kirancite{bhadkir}, Gresho and Sanicite{gresan}, P. Kiran cite{kiran}, Malashetty and Basavarajacite{malbas}, Siddheshwar and Abrahamcite{sidabr} and Siddheshwar and Pranesh cite{sidpra2} have studied the effects of gravity modulation on the onset of convection in various types of Newtonian and non-Newtonian fluids. Couple stress theory of fluids was developed by Stokescite{sto1} and represents the simplest generalization of the classical theory which allows for polar effects such as the presence of couple stresses and body couples. The study of flow of couple stress fluid has been great interest in research field due to its wide range of types and their scientific applications.

Use of couple stress in fluid in the study of mechanism of lubrication s one of the mainfront application in the field of mechanical engineering, medicine etc. Few authors I.S. Shivakumaracite{shiva}, P.G. Siddeshwar and S. Praneshcite{sidpra3} and many more have considered couple stress fluid in investigating Rayleigh-B'{e}nard convection under different situations. Pranesh and Sangeetha georgecite{prasan} studied effect of imposed time periodic boundary temperature in a dielectric couple stress fluid.

P. G. Siddheshwar and B. R. Revathicite{sidrev} studied the effect of Gravity Modulation on weakly non-linear stability of stationary convection in a dielectric fluid. It is reported in the literature that vibrations can either substantially enhance or retard heat transfer and thus drastically affect the convection.

S. Pranesh and Sameena Tarannumcite{pra2} studied the effect of gravity modulation in weak electrically conducting couple stress fluid with saturated porous layer. The main objective of this paper is to study the effects of fluctuating gravity and electric field in a weak electrically conducting couple stress fluid with a saturated porous layer on the onset of Rayleigh-B'{e}nard convection.