Question Detail
Question
Two capacitors are identical except that one is filled with air and the other with oil. Both capacitors carry the same charge. The ratio of the electric fields Eair/Eoil is:
Correct Answer
Option D is the correct answer.
Detailed Explanation
For a parallel plate capacitor, the electric field (E) is related to the charge density (σ = Q/A) and the permittivity (ε) by E = σ/ε = Q/(εA).For the air-filled capacitor, Eair = Q / (ε0 A), where ε0 is the permittivity of free space.For the oil-filled capacitor, Eoil = Q / (εoil A), where εoil = κε0 (κ is the dielectric constant of oil).Since both capacitors carry the same charge Q and have the same area A:Eair / Eoil = [Q / (ε0 A)] / [Q / (κε0 A)] = κ.The dielectric constant (κ) for oil is a value greater than 1 (typically around 2-5). Therefore, the ratio Eair/Eoil = κ will be greater than 1. This falls in the range 'between 1 and infinity'.
Hint
Recall the relationship between electric field, charge, and permittivity (dielectric constant) in a capacitor. The dielectric constant of any material (like oil) is always greater than that of a vacuum (air, which is approximately 1).