Cylindrical Capacitor Calculator

The Formula

The formula for calculating the capacitance of a cylindrical capacitor is:

$$C=\frac{2\pi {\epsilon }_0{\epsilon }_{r}L}{\ln (b/a)}$$

Where:

• C: Capacitance (in Farads, F)
• ε₀: Permittivity of free space (8.854 × 10^-12 F/m)
• ε_r: Relative permittivity (dielectric constant) of the material between the cylinders
• L: Length of the cylinders (in meters, m)
• b: Radius of the outer cylinder (in meters, m)
• a: Radius of the inner cylinder (in meters, m)

Calculation Steps

1. Identify the inner radius (a), outer radius (b), length (L), and dielectric constant (ε_r)
2. Insert these values into the formula:
3. C = (2π × ε₀ × ε_r × L) / ln(b/a)
4. Perform the calculation to get the result in Farads (F)

Example Calculation

Let's calculate the capacitance for a cylindrical capacitor with the following parameters:

• Inner radius (a) = 0.005 m
• Outer radius (b) = 0.01 m
• Length (L) = 0.1 m
• Dielectric constant (ε_r) = 2.1

$$C=\frac{2\pi \times 8.854\times {10}^{-12}\times 2.1\times 0.1}{\ln (0.01/0.005)}\approx 7.6863\times {10}^{-11}F$$

Visual Representation

This visual shows a cross-section of a cylindrical capacitor with inner and outer cylinders.