Magnetizing Force

Electrical Circuit Analysis > Magnetic Circuits

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What Is Magnetizing Force?

Magnetizing force (symbol H) — also called magnetic field intensity — is a measure of the strength of the magnetic field created by a current‑carrying conductor or coil. It describes how strongly a magnetic field can magnetize a material or establish magnetic flux in a magnetic circuit. The greater the magnetizing force, the stronger the resulting magnetic field in the material.

In simple terms, H represents the magnetic “effort” produced by electric current to set up a magnetic field along a path.

Basic Definition & Formula

The magnetizing force is defined as the magnetomotive force (MMF) per unit length of the magnetic path:

$$\bbox[10px,border:1px solid grey]{H = {m.m.f \over l}} \, \text{(At/m)}\tag{1}$$

Where:

H = magnetizing force or magnetic field intensity (A/m)
MMF = magnetomotive force (ampere‑turns, A·t)
l = length of the magnetic path (m)

MMF itself is produced by a coil of N turns with current I flowing through it: $$m.m.f=𝑁𝐼$$ Substituting for the magnetomotive force will result in

$$\bbox[10px,border:1px solid grey]{H = {NI \over l}} \, \text{(At/m)}\tag{2}$$

This means that for a given current I, more turns or a shorter length of the magnetic path leads to a higher magnetizing force.

Fig. 1: Defining the magnetizing force of a magnetic circuit .

Note in [Fig. 1] that the direction of the flux $\Phi$ can be determined by placing the fingers of the right hand in the direction of current around the core and noting the direction of the thumb. It is interesting to realize that the magnetizing force is independent of the type of core material-it is determined solely by the number of turns, the current, and the length of the core.

Example 1: Magnetizing Force in a Magnetic Circuit.

Given:

Coil with N = 100 turns
Current I = 0.5 A
Magnetic core length l = 0.25 m

Find:

Magnetizing force H

View Solution

Relationship Between Magnetic Quantities

Magnetizing force H is related to magnetic flux density B and permeability μ by:

$$\bbox[10px,border:1px solid grey]{B=\mu H} \tag{3}$$

Where:

B = magnetic flux density (tesla, T)
μ = permeability of the medium (H/m or N/A²)
$μ₀ = 4\pi \times 10^{-7} \text{ H/m}$ (permeability of free space)
$μ = μ₀μ_r$, where $μ_r$ is the relative permeability.

This key formula shows that for the same magnetizing force (H), materials with higher permeability (like iron) produce much larger flux densities than air.

Above equation can be derived as:

$$ \begin{split} H &= {mmf \over l} \\ &= {NI \over l} = {\Phi R \over l} ; \text{where} R = {l \over \mu A}\\ &= {\Phi ({l \over \mu A}) \over l}= {\Phi l \over \mu A l}\\ &= {\Phi \over A} {1 \over \mu }\\ H&= {B \over \mu }\\ B&= \mu H \end{split}$$

This equation indicates that for a particular magnetizing force, the greater the permeability, the greater will be the induced flux density. Since henries (H) and the magnetizing force (H) use the same capital letter, it must be pointed out that all units of measurement in the pages, such as henries, use roman letters, such as H, whereas variables such as the magnetizing force use italic letters, such as H.

The applied magnetizing force has a pronounced effect on the resulting permeability of a magnetic material. As the magnetizing force increases, the permeability rises to a maximum and then drops to a minimum, as shown in [Fig. 2] for three commonly employed magnetic materials.

$Variation of $\mu$ with the magnetizing force.$

Fig. 2: Variation of $\mu$ with the magnetizing force.

Example 2: Magnetic Flux Density in a Core.

Using the magnetizing force above ($H = 200 A/m$): Let’s assume an iron core with relative permeability $μ_r ≈ 5000$ Then $μ = μ₀ \times μ_r = 4\pi \times 10^{-7} \times 5000 ≈ 6.28×10⁻³ H/m$

View Solution

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