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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 (Le) and is less than its geometric length (Lg). For bar magnet, Le = 2l and Le = (5/6)Lg. for semi circular magnet Lg = πR and Le = 2R (Fig. 7).
 
88830.png
Fig. 7

Directive properties

When a magnet is suspended freely, it stays in the Earth’s NS direction (in magnetic meridian) (Fig. 8).
 
88840.png
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).
 
88851.png
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.
 
88861.png
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 –m respectively.
  • Its SI unit is Ampere × 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).
88871.png
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. 87401.png (Fig. 12).
 
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Fig. 12
  • It is a vector quantity directed from south to north.
  • Its SI unit is Ampere × meter2 or Newton-meter/Tesla and dimensions [AL2].

Cutting of a rectangular bar magnet

Suppose we have a rectangular bar magnet having length, breadth and mass as Lb, 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
 
88892.png
Fig. 13
 
Length of each part, 87409.png,
 
Breadth of each part, 87419.png
 
Mass of each part 87458.png,
 
Pole strength of each part, 87464.png, Magnetic moment of each part 87470.png
 
If, initially, moment of inertia of a bar magnet about the axes passing from center and perpendicular to its length is 87476.png, then the moment of inertia of each part I’ = I/n2.

Cutting of a thin bar magnet

For thin magnet, b = 0. So 87482.png87493.png




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