**Calculation of Capacitance**
To find the distance between the plates of a circular parallel plate capacitor, we need to calculate the capacitance first.

The capacitance of a parallel plate capacitor is given by the formula:

C = (𝜀₀ * 𝐴) / 𝑑

Where:
C is the capacitance,
𝜀₀ is the permittivity of free space (8.85 x 10⁻¹² F/m),
𝐴 is the area of the plates,
𝑑 is the distance between the plates.

**Calculation of Area**
The area of the circular plates can be calculated using the formula:

𝐴 = 𝜋 * 𝑟²

Where:
𝜋 is a constant (approximately 3.14),
𝑟 is the radius of the circular plates.

Given that the diameter of the circular plates is 40 mm, we can calculate the radius:

Radius = Diameter / 2 = 40 mm / 2 = 20 mm = 0.02 m

Substituting the radius into the formula, we find:

𝐴 = 3.14 * (0.02 m)² = 3.14 * 0.0004 m² = 0.001256 m²

**Calculation of Capacitance**
Now, we can substitute the values into the capacitance formula:

C = (8.85 x 10⁻¹² F/m) * (0.001256 m²) / 𝑑

Since the capacitance of the parallel plate capacitor is equal to that of a metallic sphere, we can use the formula for the capacitance of a sphere:

C = (4𝜋𝜀₀𝑟) / 3

Given that the radius of the metallic sphere is 1 m, we can substitute the values into the formula:

(4𝜋𝜀₀𝑟) / 3 = (8.85 x 10⁻¹² F/m) * (0.001256 m²) / 𝑑

Simplifying the equation, we find:

(4𝜋𝜀₀𝑟) / 3 = (8.85 x 10⁻¹² F/m) * (0.001256 m²) / 𝑑

**Calculation of Distance**
To find the distance, we can rearrange the equation:

𝑑 = (8.85 x 10⁻¹² F/m) * (0.001256 m²) / [(4𝜋𝜀₀𝑟) / 3]

Substituting the values into the equation, we get:

𝑑 = (8.85 x 10⁻¹² F/m) * (0.001256 m²) / [(4 * 3.14 * 8.85 x 10⁻¹² F/m * 1 m) / 3]

Simplifying the equation, we find:

𝑑 = (0.00885) * (0.001256) / [(4 * 3.14 * 0.00885) / 3]

𝑑 = 0.0000111 / 0.03716

𝑑 = 0.0002987 m

Therefore, the distance