Some Terminology and Magnetic Field

Terminology

Some terms related to magnetism are

Axis of magnet
The line joining two poles of a magnet is called the axis of the magnet. This is called the axial line outside the magnet.

Equatorial line
A line perpendicular to the axis of a magnet that passes through the center of its two poles is called the equatorial line of the magnet.

Geometric and effective lengths
The distance between two ends of a bar magnet is called its real or is observed that the effective length of a bar is 85% of its real length.

Magnetic dipole
A magnet is a system of two equal and opposite poles separated by a certain distance. Since a magnet has two poles, it is also called a magnetic dipole, being analogous to be electric dipole composed of two opposite electric charges.

Magnetic dipole moment
The magnetic dipole moment of a magnet is the product of the strength of its one pole and the distance between them. If the strength of each pole is m and the distance between them is 2l, the magnetic moment M is
$$ M = m \times 2L$$
the unit of magnetic moment is ampere meter square or joule per tesla in SI-units.

Magnetic meridian
The freely suspended magnet aligns along the north-south direction. The magnetic meridian at a place is an imaginary vertical plane passing through the axis of such bar magnet.

Horizontal component of the earth’s magnetic field
A freely suspended bar magnet sets itself along the earth’s magnetic field and it inclines downward to the horizontal at a place.The component of the earth’s magnetic field and it inclines to the horizontal direction is called its horizontal component.

Magnetic Field

The region around a bar magnet where it can exert a force on other magnets or magnetic materials is called the magnetic field. A magnetic field can be represented graphically by magnetic lines of force. If an isolated N-pole of a bar magnet is moved in the direction of the repelling force acting on it, the isolated pole will trace out a line called a magnetic line of force.

Magnetic Lines of Force

Magnetic lines of force are continuous curves, starting from the north pole to the south pole of a magnet externally and S-pole to N-pole internally. The tangent drawn at a point on such line gives the direction of magnetic field at a point. So, two lines of force never intersect each other, as two fields of the magnet are impossible at a point. In the uniform magnetic field, magnetic lines are parallel, equidistance from each other. The horizontal component of the earth’s magnetic field at a place is a uniform magnetic field. In the non-uniform magnetic field, magnetic lines are curved near the pole where the field is stronger. The magnetic lines of force are spaced so that the number per unit area is proportional to that field strength in a given area.

Magnetic Field Intensity

The strength of a magnetic field at a point is called the magnetic field intensity. It can be also defined as the force per unit north pole acting on any pole, placed at that point.

If F is the force between unit North Pole m_N at P and north pole of a bar magnet, then the magnetic field intensity at P is

\begin{align*} B &= \frac {F}{m_N} \\ \text {But, the force between the poles is } \\ F &= \frac {\mu _o}{4\pi} \: \frac {mm_N}{r^2} \\ \text {So,} \:\:\: B &= \frac {\mu _o}{4\pi } \: \frac {m}{r^2} \\ \end{align*}

Magnetic field intensity is a vector quantity. Its direction at a point is determined by the direction in which the unit north pole moves.

Reference

Manu Kumar Khatry, Manoj Kumar Thapa, et al.Principle of Physics. Kathmandu: Ayam publication PVT LTD, 2010.

S.K. Gautam, J.M. Pradhan. A text Book of Physics. Kathmandu: Surya Publication, 2003.