# Bar Magnet

A bar magnet consists of two equal and opposite magnetic pole separated by a small distance. The poles are not exactly at the ends. The shortest distance between two poles is called effective length (

*L*) and is less than its geometric length (_{e}*L*). For bar magnet,_{g}*L*2_{e}=*l*and*L*= (5/6)_{e}*L*. for semi circular magnet_{g}*L*=_{g}*Ï€**R*and*L*= 2_{e}*R*(Fig. 7).**Fig. 7**

# Directive properties

When a magnet is suspended freely, it stays in the Earthâ€™s

*NS*direction (in magnetic meridian) (Fig. 8).**Fig. 8**

# Monopole concept

If a magnet is Broken into a number of pieces, each piece becomes a magnet (Fig. 9). This in turn implies that monopoles do not exist, (i.e., the ultimate individual unit of magnetism in any magnet is called

*dipole*).**Fig. 9**

For two rods as shown in Fig. 10, if both the rods attract in Fig. 10(a) and do not attract in Fig. 10(b) then,

*Q*is a magnetic and*P*is a simple iron rod. Repulsion is the sure test of magnetism.**Fig. 10**

# Pole strength (m)

The strength of a magnetic pole to attract magnetic materials towards itself is known as pole strength. Following are the properties of pole strength:

- It is a scalar quantity.
- The pole strength of
*N*and*S*pole of a magnet is conventionally represented by +*m*and â€“*m*respectively. - Its SI unit is Ampere Ã— meter or Newton/Tesla and dimensions are [
*LA*]. - The pole strength of a magnet depends on the nature of material of magnet and the area of cross section. It does not depend upon length (Fig. 11).

**Fig. 11**

# Magnetic moment or magnetic dipole moment

It represents the strength of magnet. Mathematically it is defined as the product of the strength of pole and effective length, i

*.*e*.*(Fig. 12).**Fig. 12**

- It is a vector quantity directed from south to north.
- Its SI unit is Ampere Ã— meter
^{2}or Newton-meter/Tesla and dimensions [*AL*^{2}].

# Cutting of a rectangular bar magnet

Suppose we have a rectangular bar magnet having length, breadth and mass as

*L*,*b*, and*w*, respectively. If it is cut in*n*equal parts along the length as well as perpendicular to the length simultaneously as shown in the Fig. 13, then**Fig. 13**

Length of each part, ,

Breadth of each part,

Mass of each part ,

Pole strength of each part, , Magnetic moment of each part

If, initially, moment of inertia of a bar magnet about the axes passing from center and perpendicular to its length is , then the moment of inertia of each part

*I*â€™ =*I*/*n*^{2}.# Cutting of a thin bar magnet

For thin magnet,

*b*= 0. So