# Magnetic Circuit

## Contents

# Author: John Hawkins

## Problem Statement

Problem 2.16 from *Electric Machinery and Transformers*, 3rd ed:

A magnetic circuit is given in Figure P2.16. What must be the current in the 1600-turn coil to set up a flux density of 0.1 T in the air-gap? All dimensions are in centimeters. Assume that magnetic flux density varies as .<ref>Guru and Huseyin,Electric Machinery and Transformers, 3rd ed. (New York: Oxford University Press, 2001), 129.</ref>

## Solution

First, we note that the problem statement is incomplete. Assume that the core has a relative permeability of 500. Hence, for all magnetic sections excluding the air gap,

Also, as recommended in the text, we will neglect fringing.

The lengths and areas of each of the sections to be evaluated are given in the following table.

Section |
fg | def | ghc | dc | dabc |
---|---|---|---|---|---|

Length (m) | 0.01 | 0.555 | 0.555 | 0.48 | 1.38 |

Area (m^{2}) |
0.0032 | 0.0032 | 0.0032 | 0.0096 | 8.0e-4 |

We must now work backward from the air-gap, since the value of the flux-density is given there. We need only employ the analagous equations to Ohm's Law, KVL, and KCL. All units are standard units.

**Air Gap:**

**Right Arms:**

**Center Column:**

**Left Arm:**

**Conclusions:**

Which is the quantity we were looking for.

Calculations were performed using the following Magnetic Circuit Matlab Script.

## References

<references />

## Reviewed By

Amy Crosby