Why faraday rotation is not effective in case of circular polariation? As in case of linear polarization the plane of polarization gets rotated. Why it's not happening with circular polarization?
 A: Circular polarization is rotated just as much as linear polarization.
The catch is that the circularly polarized wave is itself “rotating” about the same axis, so the only effect is to change the phase of the wave. It's like taking a spinning wheel and rotating it by 90° — it's still spinning, and you need some notion of where it was at a given moment in time to be able to say that a change was made. 
Therefore, in order to detect the change you need to use a technique which is sensitive to phase, i.e. interferometry. Any measurement that is not comparing the rotated wave to an un-rotated wave cannot detect a difference.
A: The Faraday effect is the rotation of the polarization plane (proportional to the length $l$ and magnetic field $B$ of linearly polarized light when propagating along a magnetic field $B$ applied to a (transparent) material. Linearly polarized light can be decomposed into left and right circularly polarized light. The rotation of the linear polarization direction is due to a difference in the refractive index for right and left circularly polarized light induced by the magnetic field leading to a phase difference proportional to $l$ and $B$, which explains the rotation of the linear polarization.  Thus the influence of $B$ on the phase velocity of left and right circularly polarized light is essential to explain the Faraday effect .
