Please calculate Epsilon Naught Value using below:
The capacitance value in F is 29.5
Charge in C is 59
The electric field is 3333.333
Voltage is 2 V
Resistance 5 Amp
Plate area 2 m^2
Plate separation is 0.6 mm
The Correct Answer and Explanation is :
The permittivity of free space, denoted as ε₀ (epsilon naught), is a fundamental physical constant that characterizes the ability of a vacuum to permit electric field lines. Its standard value is approximately 8.854187817 × 10⁻¹² F·m⁻¹ (farads per meter).
In the context of a parallel plate capacitor, the capacitance (C) is related to ε₀ by the formula:
C = ε₀ × (A / d)
where:
- C is the capacitance in farads (F),
- A is the plate area in square meters (m²),
- d is the separation between the plates in meters (m),
- ε₀ is the permittivity of free space.
Given the parameters:
- Capacitance, C = 29.5 F,
- Plate area, A = 2 m²,
- Plate separation, d = 0.6 mm = 0.0006 m,
we can rearrange the formula to solve for ε₀:
ε₀ = C × (d / A)
Substituting the given values:
ε₀ = 29.5 F × (0.0006 m / 2 m)
ε₀ = 29.5 F × 0.0003 m⁻¹
ε₀ = 0.00885 F·m⁻¹
This calculated value of ε₀ is significantly higher than the accepted standard value. Such a discrepancy suggests that the initial parameters provided may not correspond to a typical parallel plate capacitor in a vacuum. In practical scenarios, especially with such high capacitance, factors like the presence of a dielectric material between the plates can greatly influence the effective permittivity. Dielectric materials have a relative permittivity (εᵣ) greater than 1, which increases the overall capacitance according to the relation:
C = ε₀ × εᵣ × (A / d)
If a dielectric is present, the calculated ε₀ would effectively represent ε₀ × εᵣ. To accurately determine ε₀, one would need to account for the dielectric’s relative permittivity.
In summary, while the formula for a parallel plate capacitor provides a method to calculate ε₀, the provided parameters lead to a value that deviates from the known constant. This suggests the influence of additional factors, such as dielectric materials, that affect the system’s capacitance. Accurate determination of ε₀ requires careful consideration of all variables involved and, ideally, controlled experimental conditions to minimize discrepancies.