Magnetic Path Length Calculation

What is Magnetic Path Length?

The magnetic path length (l_c) is the average distance that magnetic flux travels as it circulates through the core. It's a critical parameter for calculating:

Reluctance — R = l_c / (μ₀ × μ_r × A_c)
Inductance factor (A_L) — depends on l_c
Apparent permeability — μ_app = μ_r / (1 + μ_r × l_g / l_c)
Flux density — B = μ₀ × N × I / (l_c/μ_r + l_g)

Scrapless EI drawn to scale, legs upright. The window is T/2 wide and 3T/2 tall — three times as tall as it is wide, so 0.375″ × 1.125″ on an EI-75. The E is one piece, back and all three legs; only the I is separate, and the line across the top is the joint. The flux path lies between the shortest loop around one window and the longest around the outside; the mean of the two is 6T.

Flux does not follow one line — it fills the material, so every loop from the one hugging the window to the one running round the outside carries some of it. The mean path is the average of those extremes, and for scrapless EI proportions the two ends work out to a clean 4T and 8T.

Loop	Window width	Window height	Perimeter
Shortest — hugging one window	T/2	3T/2	2(T/2 + 3T/2) = 4T
Longest — tongue centreline to outer edge	3T/2	5T/2	2(3T/2 + 5T/2) = 8T
Mean path		l_c = 6T

Why not the centreline loop? Tracing the centre of the material instead — 2T up the tongue, 5T/4 across the yoke, 2T down the outer leg and 5T/4 back — gives 6.5T, and that is what a reluctance calculation returns if you assume flux is spread evenly. It is not: flux crowds to the inside of every corner, so the centreline overstates the real path. Averaging the extremes accounts for that, which is why textbooks land on 6T and why this notebook uses it. The two conventions differ by 8 %.

The window is 3T/2 long, not T. An earlier version of this page had the window height as T and summed both outer legs into a single path. Both were wrong: the window’s long dimension is exactly three times its short one — T/2 wide by 3T/2 tall, which is 0.375″ by 1.125″ on an EI-75 — and the two outer legs are parallel return paths, so a single flux loop passes through one of them, not both. The 6T result stands; the route to it did not.

EI-75

T = 0.75"

l_c = 4.5"

EI-100

T = 1.0"

l_c = 6.0"

EI-150

T = 1.5"

l_c = 9.0"

EI-200

T = 2.0"

l_c = 12.0"

1 Air Gap Effectiveness

The ratio of air gap to magnetic path length (l_g/l_c) determines how much the gap reduces the effective permeability. A longer path length means you need a larger gap to achieve the same effect.

μ_app = μ_r / (1 + μ_r × l_g / l_c)

2 Inductance Calculation

The inductance factor A_L depends on both the core area and magnetic path length. A longer path reduces A_L, requiring more turns for the same inductance.

A_L = (μ₀ × A_c) / (l_c/μ_r + l_g)

3 Core Losses

Core losses (hysteresis and eddy current) occur throughout the magnetic path. A longer path means more core material and potentially higher losses, though the flux density distribution also matters.

Non-Standard Proportions: The l_c = 6T formula assumes standard EI proportions. For cores with different aspect ratios (e.g., "long-window" or "short-stack" variations), you'll need to calculate the path length from the actual dimensions. Always check the manufacturer's specifications for non-standard laminations.

Related Calculations: The magnetic path length is used in the Class A Choke Calculator and Apparent Permeability Calculator for inductance and flux density calculations.