Question Detail
Question
A parallel plate air capacitor is made of 0.2 m square tin plates and 1 cm apart. It is connected to a 50 V battery. What is the charge on each plate?
Correct Answer
Option A is the correct answer.
Detailed Explanation
First, calculate the area of the plates: A = (0.2 m)2 = 0.04 m2. The distance between plates is d = 1 cm = 0.01 m. The permittivity of free space (for air) ε₀ ≈ 8.854 x 10-12 F/m. The capacitance C = ε₀A/d = (8.854 x 10-12 F/m * 0.04 m2) / 0.01 m ≈ 3.5416 x 10-11 F. Finally, the charge Q = C * V = 3.5416 x 10-11 F * 50 V ≈ 1.7708 x 10-9 C, which is 1.77 nC.
Hint
Recall the formula for capacitance of a parallel plate capacitor and then the formula relating charge, capacitance, and voltage. Use the correct value for permittivity of free space.