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I know that in situation II there will be a induction current; and there will be no induction current because of the constant magnetic flux in situation I; but when we move a linear conductor in a constant magnetic field it polarizes because of the charge.

In situation I why conductor does not get polarized and cause an induction EMF ?

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It does infact induce emf into the rectangular loop. That emf just doesn't flow current.
Call the left side of your rectangle side A and the right side as side B (in case I).

The side B will induce emf with the upper point as the higher potential.
The side A will also induce emf again with the upper point as higher potential.

Now when you look it as a whole the net emf is zero as the induced emf from side A is cancelled by side B. So even though emf is induced in the individual sides no current flows through them.
PS- If you connect a resistance using the upper and lower sides then current will flow in the resistor even in case 1

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  • $\begingroup$ Does higher potential means positive pole ? $\endgroup$
    – Crazy_39365
    Commented Mar 5, 2018 at 16:08
  • $\begingroup$ Yeah!!!!!!!!!!! $\endgroup$
    – SmarthBansal
    Commented Mar 5, 2018 at 16:09

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