**Magnetic intensity** at any point in the magnetic field is defined as the magnetic force acting on the unit north pole placed at that point. Let’s dive into more detailed explanation of magnetic intensity starting from magnetic pole strength.

## Magnetic Pole Strength

The force acting on the pole of a magnet in magnetic field of unit strength is called **pole strength**. Thus, magnetic pole strength is equal to the force exerted on the pole divided by the magnetic field strength. It is denoted by $m$. Its SI unit is ampere metre $\text{(Am)}$ or weber $\text{(Wb)}$.

## Force Between Two Poles of a Magnet [Coulomb’s Law]

The magnetic force acting between magnetic poles can be calculated by using the laws given by Coulomb. These laws are known as **Coulomb’s Laws in Magnetism** and are stated as follows:

- The force acting between two poles is directly proportional to their pole strengths.
- The force acting between the poles is inversely proportional to the square of distance between them.

Let two magnetic poles of strength $m_1$ and $m_2$ are placed at $r$ distance apart. Then, according to Coulomb’s law, the force $F$ between them is given by, \[F ∝ m_1m_2\] \[F ∝ \frac{1}{r^2}\]

Combining these, we get, \[F ∝ \frac{m_1m_2}{r^2}\] \[F=k\frac{m_1m_2}{r^2}\]

Where, $k$ is proportionality constant whose value depends upon the nature of the medium in which poles are placed and the system of units used.

In CGS system, $k=1$. \[\therefore F=\frac{m_1m_2}{r^2}\] In SI units, \[k=\frac{\mu}{4π}=\frac{\mu_o \mu_r}{4π}\]

Here, $μ_0 =$ permeability of vacuum or air = $4π × 10^{-7}$ $\text{Henery per metre}$ and $μ_r =$ relative permeability of the medium between poles

\[\therefore F=\frac{\mu_o \mu_r}{4π} \frac{m_1m_2}{r^2}\] In air or vacuum, $μ_r = 1$. \[\therefore F=\frac{\mu_o}{4π} \frac{m_1m_2}{r^2}\]

## Magnetic Intensity

The **magnetic intensity** at any point in the magnetic field is defined as the magnetic force acting on the unit north pole placed at that point. It is also called **magnetic field strength** or simply **magnetic field**.

Let a magnetic pole of strength $m$ be lying at $O$ and $B$ be the magnetic intensity at point $P$ at distance $r$ from the point $O$. A unit north pole $(m_0)$ is placed at $P$ where it experiences a force called **magnetic intensity**.

The magnetic force at $P$ due to pole of strength $m$ at $O$ is given by, \[F=\frac{\mu_0}{4π} \frac{mm_0}{r^2} \text{ ___(1)}\]

If $F = B$ (Magnetic Intensity) and $m_0 = 1$, then, \[B=\frac{\mu_0}{4π} \frac{m}{r^2} \text{ ___(2)}\] This is the expression for magnetic field due to a single magnetic pole.

From $(1)$ and $(2)$, \[F=B×m_0\] \[\therefore B=\frac{F}{m_0}\] Thus, magnetic intensity is defined as the magnetic force per unit pole strength.

Its unit in CGS system is oersted or gauss.

The magnetic intensity at a point is said to be one oersted or one gauss if a unit north pole placed at that point experience a force of one dyne.

Its SI units are;

- Newton per Ampere per metre $(\text{N A}^{-1}\text{m}^{-1})$
- Tesla $(T)$
- Weber per square metre $(\text{Wb m}^{-2})$ \[1 \text{ Tesla}= 10^4 \text{ Gauss or Oersted}\]

## Magnetic Dipole

Let $NS$ be a magnet whose North pole strength be $+m$ and South pole magnet be $-m$. Let the length of the magnet be $2l$ which is so small that $l^2$ becomes negligible. This system is called **magnetic dipole**. Hence, if North pole and South pole of a magnet are separated by very small but certain distance then that system is called magnetic dipole. The pole strengths of the magnet for both poles are same.

## Magnetic Dipole Moment

The product of a pole strength and magnetic length of a magnetic dipole is called magnetic dipole moment.

If $M$ is the magnetic dipole moment, then \[M=m×2l\] It is a vector quantity whose direction is along $SN$ inside the magnet.

The SI units of Magnetic Dipole Moment are;

- Weber metre $\text{(Wb m)}$
- Ampere metre
^{2}$(\text{A m}^2)$ - Jouke per Tesla $(\text{J T}^{-1})$ $(\text{Nm T}^{-1})$

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