# Physics > Magnetism and Matter

• Magnetic materials tend to point in the north-south direction
• Magnetic poles repel and unlike ones attract
• Cutting a bar magnet in two leads to two smaller magnets.
• Magnetic poles cannot be isolated.
• When a bar magnet of dipole moment m is placed in a uniform magnetic field B,
• The force on it is zero
• The torque on it is
• Its potential energy is  where we choose the zero of energy at the orientation when m is perpendicular to B.
• Consider a bar magnet of size l and magnetic moment m, at a distance r from its mid-point, where  the magnetic field B due to this bar is,

[along the axis]

=  [along the equator]

 Electrostatics Magnetism Diplole moment P m Equatorial Field for a short dipole Axial Field for a short dipole External Field: torque External Field: Energy

• Gauss's law for magnetism states that the net magnetic flux through any closed surface is zero

• The earth's magnetic field resembles that of a (hypothetical) magnetic dipole located at the centre of the earth. The pole near the geographic north pole of the earth is called the north magnetic pole. Similarly, the pole near the geographic South Pole is called the south magnetic pole. This dipole is aligned making a small angle with the rotation axis of the earth. The magnitude of the field on the earth's surface
• Three quantities are needed to specify the magnetic field of the earth on its surface – the horizontal component, the magnetic declination, and the magnetic dip. These are known as the elements of the earth's magnetic field.
•  Consider a material placed in an external magnetic field. The magnetic intensity is defined as,

• The magnetisation M of the material is its dipole moment per unit volume. The magnetic field B in the material is,

• For a linear material . So that  and  is called the magnetic susceptibility of the material. The three quantities,  the relative magnetic permeability , and the magnetic permeability  are

related as follows:

• Magnetic materials are broadly classified as: diamagnetic, paramagnetic, and ferromagnetic. For diamagnetic materials  is negative and small and for paramagnetic materials it is positive and small. Ferromagnetic materials have large and are characterised by non-linear relation between B and H. They show the property of hysteresis.

### Sample Examples

#### Question

A short bar magnet placed with its axis at  with an external field of  experiences a torque of  (a) what is the magnetic moment of the magnet? (b) What is the work done in moving it from its most stable to most unstable position? (c) The bar magnet is replaced by a solenoid of cross-sectional area  and  turns, but of the same magnetic moment. Determine the current flowing through the solenoid.

#### Solution

(a)

(b) the most stable position is  and the most unstable position is  Work done is given by

(c)

#### Question

The earth's magnetic field at the equator is approximately . Estimate the earth's dipole moment.

#### Solution

We are given that  For we take the radius of the earth . Hence,

This is close to the value quoted in geomagnetic texts.