# Magnetic Force

## What is called a Magnetic Force?

The force of attraction or repulsion exerted by a pole of magnet on another magnet or a magnetic material is called magnetic force.

The magnitude of magnetic force is determined by Coulombs law of magnetic forces.

### Coulomb’s law of Magnetic Force

Coulomb’s law of magnetic force is similar to the Coulomb’s law of electrostatic forces. Law of magnetic forces has two statements.

(1) The force of attraction or repulsion between two magnetic poles of pole strength ( q_{m_1} ) and ( q_{m_2} ) is directly proportional to the product of pole strength.

Therefore, \quad F \propto q_{m_1} \times q_{m_2} …… (1)

(2) The force between two magnetic poles is inversely proportional to the square of distance ( r ) between the poles.

Therefore, F \propto \left ( \frac {1}{r^2} \right ) …… (2)

Combining the relations from equation (1) and (2), we get –

F = K \left ( \frac {q_{m_1} q_{m_2}}{r^2} \right ) ……. (3)

Here, ( K ) is the constant of proportionality called magnetic force constant. Its value depends upon absolute magnetic permeability ( \mu_0 ) of air or free space.

In SI system, value of magnetic force constant is –

K = \left ( \frac {\mu_0}{4 \pi} \right ) = 10^{-7} \ \text {weber per ampere-metre}

Let, the units of pole strength ( q_{m_1} ) and ( q_{m_2} ) are taken in \text {ampere-metre ( A-m )} and unit of distance ( r ) is taken in ( \text {metre} ) .

Then, expression for magnetic force will be –

F = 10^{-7} \left ( \frac {q_{m_1} q_{m_2}}{r^2} \right ) \text {newton} ……. (4)

## Magnet

A magnet is a substance which when suspended freely finally rests in the North – South direction and which attracts small pieces of iron, steel, nickel, cobalt etc.

Depending upon the origin, magnets are of two types –

1. Natural magnet.
2. Artificial magnet.

### Natural Magnet

A naturally occurring iron ore called Magnetite is a natural magnet.

A magnet has certain unique properties –

1. It attract small pieces of iron and steel – It is called attractive property of a magnet.
2. A linear piece of magnetite when suspended freely, it comes to rest along geographical North – South direction – It is called directive property of a magnet.

Magnetite is an oxide of iron with the chemical formula Fe_3O_4 . This natural magnet is also known as Black stone or Load stone or Kissing stone. It has following properties –

1. Natural magnets are weak magnets.
2. A natural magnet is irregular in shape.
3. Earth itself behaves as a natural magnet having geographical North and South poles.

### Artificial Magnet

The man-made magnets are known as Artificial magnets.

Since, a natural magnet is very weak magnet and it is of irregular shape, artificial magnets are produced for specific purposes. Artificial magnets are produced by two methods –

1. When ordinary iron pieces are rubbed with magnets, they acquire the attractive and directive properties of a magnet.  This process is called magnetization. The magnets so produced are known as artificial magnets.
2. Magnetization can also be produced by passing an electric current through a coil wound over a piece of iron bar. Magnets produced by such method are called electromagnets.

Advantages of artificial magnets are –

1. An artificial magnet is stronger than the natural magnet.
2. It can be made of any desired shapes and sizes.
3. Bar magnets magnetic needle, U shape magnets etc. are common examples of man-made magnets.

## Properties of Bar Magnet

A rectangular piece of magnet having equal pole strength at its two ends is called a bar magnet.

A bar magnet has following properties –

1. A magnet has property of alignment.
2. It has property of attraction between unlike poles of two magnets or between a magnet and a magnetic material.
3. A magnet has unique property of repulsion.
4. It has property of paired poles. It poles can’t be separated with each other.
5. Magnets have property of producing induction into other magnetic materials.

### Property of alignment

A magnet, when suspended freely, finally comes to rest such that its one end always points towards geographical North pole and other end points towards geographical South pole. This is called the property of alignment of a magnet.

The end which points towards geographical North is called North pole and the end which points towards the geographical South is called South pole of the magnet.

A line joining North and South poles of magnet is called magnetic axis and a vertical plane passing through this line is called magnetic meridian.

### Property of attraction

Poles of a magnet have property to attract small pieces of magnetic material like iron, steel, cobalt, nickel etc. This is called attractive property of a magnet.

This property is also exhibited between unlike or dissimilar magnetic poles of two different magnets. The strength by which a magnetic pole attracts to magnetic materials, is known as pole strength.

### Property of repulsion

Like or similar magnetic poles of two different magnets have a property to repel each other. This property is called property of repulsion of a magnet.

When South pole of a magnet is brought near to the South pole of an other magnet, repulsion takes place. But when South pole of one magnet is brought near to the North pole of other magnet, attraction takes place.

### Property of pairing of poles

Magnetic poles always exist in pairs on same magnet body i.e., South pole and North pole of a magnet can not be separated.

If a bar magnet is cut into two pieces, it will result into two complete magnets. Each of the two pieces will now have both North as well as South poles.

Thus magnetic mono-poles doesn’t not exist.

### Repulsion is a surer test

Repulsion is a surest test of magnetism.

This can be explained with following task example.

TASK – Suppose, we have given two identical bars and asked to find which one or both of them are magnet or not?

We know that, a magnet attracts an ordinary iron piece as well as an unlike pole of another magnet. Thus in distinguishing a magnet bar and a non magnet bar, attractive property of magnet is not helpful. We will perform the following activity.

1. One of the bar is held in right hand and the other in left hand.
2. Now slowly bring the ends of both the bars closer to each other end to end.
3. In doing so, we can felt either of the following effects –
1. Attraction is felt between the ends of bars – This will conclude that either one bar is magnet or both of the bars are magnets. Now polarity of one bar is reversed and checked again. If still attraction persist, this concludes that only one bar is magnet. ( Because attraction occur (1) between a magnet and a non magnet (2) between two magnets of unlike poles ). But, which bar is magnet? To find this, we have to perform repulsion test with each bar and a third bar magnet.
2. Repulsion is felt between the ends of bars – This will conclude and ensures that, both of the bars are magnets. ( Because repulsion only occur between two like poles of magnets. )
3. Attraction or repulsion, nothing is happened – This will conclude that none of the bars are magnets, i.e. both bars are ordinary iron bars.

Thus, from above activity we can say that, repulsion is the only surest test for distinguishing between an iron piece and a magnet.

### Property of induction

When a piece of ordinary magnetic material is brought near to a bar magnet, it acquires the property of a magnet without any physical contact.

Such type of magnetism is called induced magnetism.

## Pole strength of a Magnet

From Coulomb’s law of magnetic forces, we have –

F = 10^{-7} \left ( \frac {q_{m_1} q_{m_2}}{r^2} \right )

The SI unit of pole strength is ampere-metre (Am) or newton / tesla (NT -1)

Let, ( q_{m_1} = q_{m_2} = q_m ) and ( r =1 ) . In that case if the force of attraction  ( F = 10^{-7} N )

Then, \quad q_m = \pm 1

Thus, pole strength is said to be of ( 1 \ \text {A-m} ) if the pole repels equal and similar pole with a force of ( 10^{-7} \ \text {newton} ) when placed ( 1 \ m ) away from it in vacuum.