---
title: "Circular core, current for 1 T air gap (mean length)"
subject: "Electrical Machines"
chapter: 1
key: "semester_4/electrical_machines:core-airgap-current-4000-length"
source: https://www.bctengineer.com/q/semester_4/electrical_machines/core-airgap-current-4000-length
site: BCT Engineering
---

# Circular core, current for 1 T air gap (mean length)

Electrical Machines · Chapter 1: Magnetic Circuits and Induction

- Asked in: 2069 Bhadra
- Video: [NEW TOPIC : IRON RING WITH AIRGAP | UNIT : MAGNETIC CIRCUIT IN HINDI (LECTURE 22)  @TIKLESACADEMY](https://www.youtube.com/watch?v=HZb3EGXqjoQ) — TIKLE'S ACADEMY
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machines/core-airgap-current-4000-length
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines/chapter-1

## Question

A magnetic circuit consists of a circular iron core having mean length of 10 cm and cross-sectional area of 100 mm$^2$. The air gap is 2 mm and the core has 600 turns of winding. Calculate the magnitude of current to be passed through the winding to produce air gap flux of 1 Tesla. Given $\mu_r = 4000$.

## Short answer

The mmf is the sum of iron and air-gap contributions. For a 10 cm mean magnetic path (including 2 mm gap) and 600 turns, the current needed to produce 1 T is approximately 2.69 A.

## Answer

**Given:** mean length of magnetic circuit $= 10$ cm (taken to include the gap), $A = 100$ mm$^2 = 10^{-4}$ m$^2$, $l_g = 2$ mm, $N = 600$, $B_g = 1$ T, $\mu_r = 4000$.

Neglecting leakage and fringing, $B$ is 1 T in both iron and gap.

**Path lengths**

$$
l_i = 0.100 - 0.002 = 0.098\ \text{m}
$$

**Mmf**

$$
\begin{aligned}
F_i &= \frac{B l_i}{\mu_0\mu_r} = \frac{0.098}{4\pi\times10^{-7}\times4000} = 19.50\ \text{AT} \\
F_g &= \frac{B l_g}{\mu_0} = \frac{0.002}{4\pi\times10^{-7}} = 1591.5\ \text{AT} \\
F &= 1611.0\ \text{AT}
\end{aligned}
$$

**Current**

$$
I = \frac{1611.0}{600} = 2.685\ \text{A}
$$

If the 10 cm is taken as the iron length only (gap extra), $F_i = 19.9$ AT and $I = 2.686$ A, so the answer is the same to three figures.

**Answer: $I \approx 2.69$ A**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. If 10 cm is the total mean length including the 2 mm gap, what is l_i?
   A. 10 cm
   B. 9.8 cm
   C. 10.2 cm
   D. 8 cm
   Answer: B. l_i = 0.100 - 0.002 = 0.098 m. (Key point: Iron length)

2. What is the gap mmf for B = 1 T and 2 mm?
   A. 19.5 AT
   B. 159 AT
   C. 1591.5 AT
   D. 15915 AT
   Answer: C. F_g = B l_g/mu_0 = 0.002/(4 pi e-7) = 1591.5 AT. (Key point: Gap mmf)

3. Why is the answer almost unchanged whether 10 cm includes the gap or not?
   A. The iron mmf is tiny compared with the gap mmf
   B. The gap has no mmf
   C. The iron has no mmf
   D. The area cancels
   Answer: A. Iron needs only about 20 AT against 1591 AT for the gap, so the 2 mm change hardly matters. (Key point: Insensitivity to interpretation)

## Close variants set in other exams

- [Circular core, current for 1 T air gap (mean diameter)](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Acore-airgap-current-4000-diameter) — Electrical Machines, chapter 1, asked 2×

## Related in Electrical Machines

- [Core with 4 mm air gap: inductance and flux](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Acircular-core-4mm-gap-inductance-flux) — Electrical Machines, chapter 1
- [DC current for iron rod ring with 4 mm air gap](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Airon-rod-200sqmm-4mm-500turns-250mwb) — Electrical Machines I, chapter 1
- [Number of turns for iron ring with air gap](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Airon-ring-1p25m-turns-0p5wb) — Electrical Machines I, chapter 1, asked 2×
- [DC current for iron ring with 4 mm air gap](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Airon-ring-1p5m-4mm-500turns-current) — Electrical Machines I, chapter 1
- [Reluctances and air gap flux of two-winding core](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Atwo-winding-core-reluctance-airgap-flux) — Electrical Machines I, chapter 1
- [DC current for ring core with 2 mm air gap](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aring-5p5cm-3p5cm-airgap-0p3mwb) — Electrical Machines I, chapter 1

## Related in other subjects

- [Iron core current for 1 T air-gap flux](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Airon-core-air-gap-1-tesla) — Electrical Machine, chapter 1, asked 2×
- [Iron ring current for 0.8 Wb air-gap flux](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Airon-ring-air-gap-0-8-wb) — Electrical Machine, chapter 1, asked 2×
- [Number of turns of iron-core inductor](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Ainductor-turns-iron-core-500mh) — Basic Electrical Engineering, chapter 4
- [Circular core inductance and flux](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Acircular-core-inductance-flux) — Electrical Machine, chapter 1