Polar molecules are the molecules :

The correct option is: having a permanent electric dipole moment.

To understand why this is the correct answer, let us break down the molecular structure and behavior of polar molecules step-by-step:
1. Definition of a Polar Molecule: A polar molecule is a molecule in which the centers of positive charges (protons) and negative charges (electrons) do not coincide. This separation of charges creates a permanent separation of charge, which is defined as a permanent electric dipole moment.
2. Permanent vs. Induced Dipole Moment:
- Polar molecules possess a permanent electric dipole moment even in the absence of any external electric field. Examples include water ($H_{2}O$) and hydrochloric acid ($\mathrm{HCl}$).
- Non-polar molecules (like $O_2$ or $N_2$) have symmetric charge distributions and thus have a zero dipole moment in their normal state. They can only acquire an induced dipole moment when an external electric field is applied, which displaces the positive and negative charge centers relative to each other.
3. Analyzing the Options:
- "acquire a dipole moment only when magnetic field is absent.": This is incorrect because dipole moments in polar molecules are electric in nature and are permanent, regardless of magnetic fields.
- "having a permanent electric dipole moment.": This is correct, as it is the defining characteristic of polar molecules.
- "having zero dipole moment.": This describes non-polar molecules, not polar molecules.
- "acquire a dipole moment only in the presence of electric field due to displacement of charges.": This describes the behavior of non-polar molecules (induced polarization), not polar molecules.