The magnetic field from the center of a circular loop of radius R along the axis is given by
\(\vec { B } =\frac { { \mu }_{ 0 }I }{ 2 } \frac { { R }^{ 2 } }{ ({ R }^{ 2 }+{ z }^{ 2 })^{ \frac { 3 }{ 2 } } } \hat { k } \)
At larger distance z >> R, therefore R² + z² ≈ z²,
we have
\(\vec { B } =\frac { { \mu }_{ 0 }I }{ 2 } \frac { { R }^{ 2 } }{ { z }^{ 3 } } \hat { k } \)               ........(1)
Let A be the area of the circular loop A = πR². So rewriting the equation (1) in terms of the area of the loop, we have
\(\vec { B } =\frac { { \mu }_{ 0 }I }{ 4\pi } \frac { { R }^{ 2 } }{ { z }^{ 3 } } \hat { k } \)
\(\vec { B } =\frac { { \mu }_{ 0 } }{ 4\pi } \frac { 2IA }{ { z }^{ 3 } } \hat { k } \)              .......(2)
Comparing equation (2) with equation (1) dimensionally, we get
p_m = IA
where P_m is called a magnetic dipole moment. In vector notation,
\(\vec { { p }_{ m } } =I\vec { A } \)       .........(3)
This implies that a current - carrying circular loop behaves as a magnetic dipole of the magnetic moment \(\vec { { p }_{ m } } \) So, the magnetic dipole moment of any current loop is equal to the product of the current and area of the loop.

(i) Magnetic field lines are continuous closed curves. The direction of magnetic field lines is from the North pole to the South pole outside the magnet and South pole to the North pole inside the magnet.
(ii) The direction of a magnetic field at any point on the curve is known by drawing a tangent to the magnetic line of force at that point.
(iii) Magnetic field lines never intersect each other.
(iv) The degree of closeness of the field lines determines the relative strength of the magnetic field. The magnetic field is strong where magnetic field lines crowd and weak where magnetic field lines thin out.

(i) A freely suspended bar magnet will always point along the north-south direction.
(ii) A magnet attracts another magnet or magnetic substances towards itself. The attractive force is maximum near the end of the bar magnet. When a bar magnet is dipped into iron filling, they cling to the ends of the magnet.
(iii) When a magnet is broken into pieces, each piece behaves like a magnet with poles at its ends.
(iv) Two poles of magnet have pole strength equal to one another.
(v) The length of the bar magnet is called geometrical length and the length between two magnetic poles in a bar magnet is called magnetic length. Magnetic length is always slightly smaller than geometrical length.

(i) Magnets are classified into natural magnets and artificial magnets.
(ii) For example, iron, cobalt, nickel, etc. are natural magnets.
(iii) Strengths of natural magnets are very weak and the shapes of the magnet are irregular.
(iv) Artificial magnets are made by us in order to have desired shape and strength.
(v) If the magnet is in the form of rectangular shape or cylindrical shape, then it is known as bar magnet.