Each plate of a parallel-plate air capacitor has an area of 0.0010 m2, and the separation of the plates is 0.050 mm. An electric field of 7.4 × 106 V/m is present between the plates. What is the capacitance of this capacitor?

The capacitance of the parallel-plate air capacitor is approximately 1.77 × 10⁻¹⁰ Farads.

To calculate the capacitance of the parallel-plate air capacitor, we can use the formula:

C = ε₀ * (A / d)

where C is the capacitance, ε₀ is the permittivity of free space (approximately 8.85 × 10⁻¹² F/m), A is the area of each plate, and d is the separation between the plates.

Given:

Area of each plate (A) = 0.0010 m²

Separation between the plates (d) = 0.050 mm = 0.050 × 10⁻³ m

Electric field (E) = 7.4 × 10⁶ V/m

Now, let's substitute the given values into the formula:

C = (8.85 × 10⁻¹² F/m) * (0.0010 m² / 0.050 × 10⁻³ m)

Simplifying the expression:

C = 8.85 × 10⁻¹² F * (0.0010 m² / 0.050 × 10⁻³ m)

C = 8.85 × 10⁻¹² F * 20

Calculating the capacitance:

C = 1.77 × 10⁻¹⁰ F

Therefore, the capacitance of the parallel-plate air capacitor is approximately 1.77 × 10⁻¹⁰ Farads.

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