After a decade of using a microwave oven in my house I figured out I never cared to connect the grounding cable. So my question is regardless of electrical shock risk, does the Microwave Faraday cage shielding work without a ground connection? I am afraid the shielding require a ground connection to work and hence a lot of microwave radiation leaked. Is that correct?
[Physics] Microwave Faraday cage shielding
microwaves
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Actually, cell phones do work in Faraday cages these days. What happens is that the conductor in the cage is not ideal, and there is some amount of leakage of electromagnetic radiation to and from the inside of the cage, specially at high frequencies. In order for the cage to be perfectly blocking it would need to have no holes at all (hence it is no longer a cage, but a box) and made of a perfectly conducting material, such as a superconductor, with a thickness larger than about 3 times the penetration depth of the radiation for that material.
The sizes of the holes need to be smaller than the wavelength of the EM radiation, so that you can neglect the holes. The wavelength is inversely proportional to the frequency of the radiation, thus, Faraday cages are more efficient for low frequencies, such as a DC field or lightning. This is why light, which is also a form of electromagnetic radiation, can pass through the centimeters-sized holes of an ordinary cage.
Two things are going on. First - the conductivity of the shielding of the microwave oven is "only so good": the skin effect in particular results in the electrical currents running in only a very superficial layer of the conductor, and this means there is some phase lag (and incomplete reflection, i.e. some transmission of power).
Second, gaps do occur. In a well designed microwave the gaps have compliant conductive seals; but if these lose their springiness I can see how currents flowing around the gap will result in re-emission of microwave energy. You don't need a 2D opening: just a gap that is "long and thin" is sufficient to act as an antenna. Where "long" is a few cm (1/4 of a wavelength). See for example this diagram:
from http://www.interferencetechnology.com/in-situ-emc-testing-using-surface-current-sense-wires-1/ which describes some of the techniques behind using such an "antenna".
Best Answer
The grounding cable is to prevent a surge in current from producing a shock danger at the case of the appliance. It has nothing to do with the Faraday shielding. Metal absorbs microwave radiation whether in an electrical appliance or not, and even the glass window is an effective Faraday shield because it has embedded within it a wire grid whose holes are much smaller than the 'wavelength' of the microwaves, rendering it opaque to that frequency.