Magnetic Intensity- Definition, Units, Formula, Hysteresis Loop (2024)

NTA recently extended the last date of JEE Main 2020 and this paves the way for the students to fill the application form, if not yet. Today, we’re covering an important topic from JEE Main Physics Syllabus i.e. the Magnetic Field Intensity.

Magnetic Intensity

Magnetic field intensity (H) at any point in the magnetic field is defined as the force experienced by the unit north pole at that point. In simple terms, it is a measure of how strong or weak any magnetic field is. The SI unit of magnetic field intensity is Ampere/meter (A/m).

According to David C Jiles, magnetic field intensity definition is as follows:

“A magnetic field intensity or strength of 1 ampere per meter is produced at the center of a single circular coil of conductor of diameter 1 meter when it carries a current of 1 ampere.”

The magnetic flux density (B) is the magnetic moment developed per unit volume of a material when placed in a magnetizing field. The relation between the magnetic flux density and the magnetic field intensity is given by :

B = μH

Sometimes, the definition of magnetic flux intensity/density and magnetic field intensity can be confusing. Magnetic flux density is the measure of the number of magnetic lines of flux that passes through a point on a surface. It is measured in tesla and is a vector quantity.

Apart from units, B and H are the same in a vacuum. The difference between the two arises in a magnetized material. Inside a magnetic material, the total magnetic field is the resultant of B_O and B_M produced due to magnetization.

B = B_O + B_M

= μH + μM

= μ(H+M)

Hysteresis Loop

When a ferromagnetic sample is placed in a magnetizing field, it gets magnetized by magnetic induction. As the magnetic field intensity H varies, magnetic induction B does not vary linearly. The permeability μ is not constant and varies with H. it also depends on the past history of the sample.

If magnetizing field intensity H is gradually decreased to zero, B decreases but along a new path ‘ab’. It is found that magnetic induction B is not zero even after H becomes zero. That means the magnet is not demagnetized even when the magnetizing field has been removed. The magnetic induction left behind in the sample is called residual magnetism or retentivity.

The value of reverse magnetizing field intensity H required for the residual magnetism of a sample to become zero is called the coercivity of the sample.

This graph drawn to depict the relation between magnetic field intensity H and magnetic flux density B for a material placed in the magnetizing field is known as the hysteresis curve. And the closed area ‘abcdef’ which represents the cycle of magnetization of a ferromagnetic sample is called its hysteresis loop.

Calculation of Magnetic Field Intensity at Different Points

1. Axial Point

The force exerted by the north pole of the magnet at point P is :

Similarly, the force exerted by a south pole at point P is :

Strength of the magnetic field at point P is :

B_axial = F – F1

( 2l = m, magnetic dipole moment)

2. Equatorial point

As magnitudes of vertical components of F and F1 gets canceled, their horizontal components will add up.

So

B_equa = Fcosθ + F1cosθ

= 2Fcosθ

=

If the magnet is very short,

Key Points

1. A magnetic field intensity or strength of 1 ampere per meter is produced at the center of a single circular coil of conductor of diameter 1 meter when it carries a current of 1 ampere.
2. The magnetic flux density (B) is the magnetic moment developed per unit volume of a material when placed in a magnetizing field.
3. In vacuum, the relation between H and B is given by B = μH. Where μ is the permeability constant.
4. For a magnetic material placed inside a magnetic field, the relation becomes μ(H+M). Where M is the magnetic moment per unit volume.
5. The relation drawn between B and H is known as the Hysteresis curve.
6. The area within the B-H curve depicts the energy dissipated per unit volume in the material when it is carried through a cycle of magnetization.
7. Magnetic field intensity formula at an axial point is
8. Magnetic flux intensity formula at an equatorial point is

This was all about the concept of magnetic intensity. Please remember this is a very important topic considering the JEE Main Exam. Get some practice of the same on our free Testbook App. Download Now!