Step 1: Understanding the Question:
The question asks to identify the material with the highest ability to polarize in an electric field, represented by its dielectric constant ($\epsilon_r$ or $k$).
Step 2: Detailed Explanation:
Dielectric Constant: It is a measure of a material's ability to store electrical energy in an electric field.
Barium Titanate ($BaTiO_3$): This is a ferroelectric ceramic material. It has an exceptionally high dielectric constant, often ranging from 1,000 to over 10,000 depending on grain size and temperature.
Its high value is due to the spontaneous displacement of the titanium ion within the oxygen octahedron of its perovskite crystal structure, leading to large dipole moments.
Comparison values:
Rubber: Dielectric constant $\approx$ 2 to 4.
Alumina ($Al_2O_3$): Dielectric constant $\approx$ 9 to 10.
Glass: Dielectric constant $\approx$ 4 to 10 (depending on composition).
Step 3: Final Answer:
$BaTiO_3$ has the highest dielectric constant among the given choices.