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 E_air/E_oil is: A)between 0 and 1 B)0 C)1 D)between 1 and infinity E)infinite

Question

Quizplus · Accepted Answer

The electric field (E) in a capacitor is given by E = V/d, where V is the voltage across the capacitor and d is the distance between the plates. The capacitance (C) is given by C = εA/d, where ε is the permittivity of the material between the plates, A is the area of the plates, and d is the distance between the plates. For the same charge (Q) on both capacitors, Q = CV, so V = Q/C. Since the capacitors are identical except for the dielectric material, A and d are constant, but ε changes. The oil-filled capacitor has a higher permittivity (ε_oil) than air (ε_air), leading to a higher capacitance. Therefore, for the same charge, the voltage across the oil-filled capacitor will be lower, and so will the electric field. The ratio of electric fields (E_air/E_oil) will be greater than 1 because ε_oil > ε_air, leading to E_oil < E_air for the same charge.

Two Capacitors Are Identical Except That One Is Filled with Air