Magnetic Circuit Air Gaps

Electrical Circuit Analysis > Magnetic Circuits

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in Mar 2026

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Introduction

An air gap is a non-magnetic section present in a magnetic circuit. It is usually connected magnetically in series with the remaining parts of the circuit. The presence of the air gap allows the magnetic flux to pass through a region of very low permeability compared with the magnetic core.

Depending on the application, the gap may contain air, gas, vacuum, plastic, or other non-magnetic materials. Even though the gap may be small, it has a significant effect on the performance of the magnetic circuit because the permeability of air is much lower than that of ferromagnetic materials.

Fig.1:

Fig.2: Air gaps: (a) with fringing; (b) ideal.

In electrical machines such as motors, relays, and measuring instruments, air gaps are intentionally introduced in the magnetic path to control magnetic flux and mechanical motion.

Flux Distribution in Air Gap

In practical magnetic circuits, the magnetic flux spreads slightly when it passes through the air gap. This spreading of flux lines outside the core area is called the fringing effect.

For simplified analysis, the fringing effect is often neglected and it is assumed that the flux distribution is uniform across the air gap.

Under this assumption, the magnetic flux density in the air gap is given by

$$B_g = \frac{\Phi_g}{A_g}$$

where

$B_g$ = flux density in the air gap
$\Phi_g$ = magnetic flux through the gap
$A_g$ = cross-sectional area of the air gap

In most cases $$ \Phi_g = \Phi_{core} $$ and $$ A_g = A_{core} $$

Magnetizing Force in Air Gap

For practical engineering calculations, the permeability of air is taken to be equal to the permeability of free space.

The magnetic field intensity in the air gap is therefore given by

$$H_g = \frac{B_g}{\mu_0}$$

where $$ \mu_0 = 4\pi \times 10^{-7} $$

Substituting this value,

$$H_g = \frac{B_g}{4\pi \times 10^{-7}}$$

This can also be written approximately as

$$H_g = (7.9 \times 10^{5}) B_g \; \text{At/m}$$

The magnetomotive force (mmf) drop across the air gap is

$$\text{MMF}_{gap} = H_g l_g$$

where $l_g$ is the length of the air gap.

Example: Magnetic Circuit with Air Gap

Example 1: Find the value of $I$ required to establish a magnetic flux of $\Phi = 0.75 \times 10^{-4} \, \text{Wb}$ in the series magnetic circuit of [Fig. 3].

Fig. 3: Relay for Example 1.

Solution: The flux density for each section is

$$B = {\Phi \over A}$$

$$B = {0.75 \times 10^{-4} \over 1.5 \times 10^{-4}} = 0.5 \,T$$

From the B-H curves

$$H \text{(cast steel)} = 280 \, At/m$$

Applying Eq. (3),

$$ \begin {split} H_g &= (7.9 \times 10^5)B_g \\ &= (7.9 \times 10^5) (0.5T) = 3.98 \times 10^5 \,\text{At/m}\\ \end{split}$$

The mmf drops are

$$H_{core}l_{core} = (280 At/m)(100 \times 10^{-3} m) = 28 \text{At}$$

$$H_gl_g = (3.98 \times 10^5 At/m)(2 \times 10^{-3} m) = 796 \text{At}$$

Applying Amperes circuital law,

$$\begin{split} NI &= H_{core}l_{core} + H_gl_g\\ &= 28 At + 796 At\\ (200 t)I &= 824 At\\ I &=4.12 A\\ \end{split} $$

Conclusion

Air gaps play an important role in magnetic circuit design. Because the permeability of air is much lower than that of magnetic materials, the air gap introduces significant reluctance in the magnetic path. This increases the magnetomotive force required to establish the desired magnetic flux.

Despite increasing reluctance, air gaps are intentionally used in many electrical devices such as motors, relays, and inductors to control magnetic flux, prevent saturation, and allow mechanical movement within magnetic systems.

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