B Field Vs H Field: Detailed Insight and Facts

B field and H field are two slightly related terms but they are used for two different fields. In this post, we’ll look at the differences between B field vs H field. 

The actual magnetic field within a substance is represented by the magnetic flux density, which is the pattern of magnetic field lines, or flux, per unit cross-sectional area. On the other hand, the H field is magnetic field strength that is caused by an exogenous current and is not inherent in the substance.

Vector B is used to depict the magnetic flux density. H is the vector that represents the magnetic field strength or magnetic field intensity. The SI unit of measurement is amperes per meter. 

In simple words, one can understand magnetic field strength H, as a magnetic field that is generated due to the flow of current in a wire, while magnetic flux density B can be understood as a total magnetic field containing magnetization M that is created by magnetic properties of a substance in the field.

The magnetizing field H is fairly modest when a current runs in a wire wrapped around a soft-iron cylinder, yet the real mean magnetic field is rather strong. 

Magnetic field strength formula

Magnetic field strength is calculated by the formula given below;  


Here H is magnetic field strength, B is magnetic flux density, μ is magnetic permeability and M is magnetization.    

It is expressed in SI units as Amperes per meter.  

Magnetic flux density formula  

Magnetic flux density can be calculated by the formula given below;  

B= Hμ

Here B is magnetic flux density, μ is magnetic permeability and H is magnetic field strength.   

It is expressed in Weber per square meter, which is the same as Tesla [T].  

The relation between B, H, and I  

As we know that magnetic strength, symbolized by H, is a number that characterizes magnetic phenomena from the perspective of their magnetic fields. The magnetic field strength at a particular position can be expressed in terms of H. The magnetic field and magnetic strength, as well as the permeability of space, is determined by the intensity of magnetization.  

So magnetic strength is a term used to describe magnetic phenomena concerning the magnetic field. The magnetic strength ‘H’ is calculated using the equation B=μ0H …………………(1)

Here H shows magnetic field strength and B is a magnetic field.   

Magnetic field B can be expressed as B= μ0(H+MZ) ……………(2)

Here MZ  is magnetization.   

Mathematically magnetization and magnetic strength are related by this formula given below; 

MZ= χH …………..(3)

Here χH is magnetic susceptibility.  

Magnetic susceptibility for paramagnetic materials is low and positive, while magnetic susceptibility for diamagnetic materials is low and negative. We may express equations 1,2 and 3 as given below; 

B= μ0(1+χH)……………(4)

That is how B= μ0 μr H

As μ= μ0 μr

So, B= μ H

Where μr=(1+χ)

μr is a dimensionless quantity and also called relative magnetic permeability of the material.   

If I is the magnetization intensity and B is the magnetic field within the material, then magnetic strength H in vector form may be represented as below;   

H= (B\ μ0) -I

Again simplifying,  


So the relation between B, H and I is B=μ0(H+I)

Hysteresis loop (B-H Graph)   

The Hysteresis curve is obtained by plotting Magnetization M or Magnetic Field B as a relation of Magnetic Field Strength H (i.e. M-H or B-H graph). A ferromagnetic material’s permeability can be negative or positive and can vary from zero to infinity.   

Hysteresis is described as the delay in a variable attribute of a system concerning the effect that produces it when that effect changes. In ferromagnetic materials, the magnetic flux density B falls behind the fluctuating exterior magnetizing field strength H.  The hysteresis curve is generated by displaying the graph of B-field versus H by putting the material through a full cycle of H values, as shown below 

Hysteresis loop of B field vs H field
Hysteresis loop of B field vs H field

Assume a ferromagnetic material sample that has not been magnetized. At O, the magnetic field strength H is originally zero. When H is raised steadily over time, magnetic induction B rises nonlinearly along the magnetization curve (OACDE). Nearly all of the magnetic domains are oriented parallel to the magnetic field at point E.  

A further rise in H does not result in a boost in B. The magnetic saturation point of a substance is designated by E. Permeability values produced from the equation μ=B\H along the curve is usually positive and span a large range. At the “knee” (point D) of the curve, the greatest permeability that is 105μ0 occurs.

After that H is reduced to zero and B decreases from its saturation point E to that point F. Some magnetic domains fail to keep alignment but some magnetic domains keep their alignment and. This indicates that the material still has some magnetic flux density B. 

The curve for decreasing H values (demagnetization curve EF) is displaced by a quantity FO from the curve for rising H values (that is magnetization curve OE). The quantity of FO shift is referred to as retentivity. 

At point “I,” B achieves saturation in the opposite direction as H increases to high negative values. Almost all magnetic domains are aligned in opposite directions to point E of positive saturation. H is switched from its most negative to its most positive value. Then B arrives at point “J.” This point demonstrates residual magnetism of the same order as for positive H values (OF=OJ).  

H is grown in a positive way from zero to maximum. Then, at point “K,” B reaches zero. It does not, therefore, travel through the graph’s origin. The quantity of field H necessary to cancel out the residual magnetism OJ maintained in the reverse way is shown by OK. 

H is raised from location k in a positive direction, then B approaches saturation at point “E” and the loop is closed. 

Frequently asked questions FAQs  

Q. What is retentivity?   

A measurement of the remaining flux density related to a magnetic material’s saturation.   

Whenever a substance’s magnetization is removed following saturation, it can still preserve a little quantity of magnetic field (The value of B at point E on the hysteresis curve). 

Q. What is residual magnetism or residual flux?   

The remnant magnetism and retentivity are the identical when the material is magnetized to saturation.

The magnetic flux density B remains in the substance when the magnetizing field strength H is zero. It might be lower than the retentivity value.  

Q. What is Coercivity?  

It refers to the amount of reversed magnetizing field strength that must be given to a magnetic substance for the magnetic flux density of ferromagnetic material to revert to zero after saturation. (On the hysteresis curve, the value of H at point G.) 

Q. What is Reluctance?

It refers to a ferromagnetic material’s resistance to the formation of a magnetic field. The impedance in an electrical circuit is equivalent to reluctance. 

Q. What is Permeability?

The flexibility with which a magnetic flux may be created in a material is measured by its permeability. In the B-H graph, X is negative in the II and IV quadrants and positive in the I and III quadrants (i.e. the Hysteresis curve).

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