Inductance of a Straight Wire

Overview:
Even a simple length of wire can exhibit inductance, or more specifically, self-inductance. This calculation determines the inductance of a length of wire based on its diameter and length.

- The self-inductance of a wire is often not measured individually since it usually forms part of a circuit's loop.
- This tool allows you to input the diameter and length of the wire to calculate the inductance. The result is provided in nano henries (10⁻⁹ H).

Equation:
The inductance of the wire is calculated using the following formula:
L_wire = 2l * ln { [(2L / D) * (1 + sqrt(1 + (D / 2L)²))] - sqrt(1 + (D / 2L)²) + (μ / 4) * (D / 2L) }

Where:

• L_wire: Inductance of a straight wire in henries (H).
• D: Diameter of the wire in cm.
• L: Length of the wire in cm.
• μ: Permeability of the wire.

Key Notes:

• The equation is sourced from "Inductance Calculations" by F. W. Grover.
• This formula assumes a cylindrical wire with uniform diameter and length.

Practical Applications:

• Useful for designing circuits where precise inductance values are required, especially in RF and high-frequency applications.
• Provides a straightforward method to estimate inductance in basic wiring setups.
• Helps engineers calculate the impact of inductance in cable runs or single-conductor transmission lines.

Example Calculation:
Consider a wire with:

• Diameter (D): 1 cm
• Length (L): 50 cm
• Permeability (μ): 1 (assuming a non-magnetic wire)

The inductance can be computed by substituting these values into the formula. Ensure the proper units and logarithmic calculations are applied for accuracy.