Show the magnetic dipole moment in terms of pole strength.

Explanation

The strength of magnetic pole is called pole strength.
Magnetic dipole moment per unit length of magnet is called pole strength of magnet.
Charge `q` is like that in equations of static electricity, likewise pole strength is in magnetism.
Pole strength is denoted by `q_(m)` or `P`.
Pole strength depend on the type of material of magnet, its magnetization position and area of cross section (A) of magnet.
It is a scalar quantity.
The unit of pole strength is ampere meter (Am).
If the length of bar magnet is `(2l)` and pole strength `q_m` then magnetic dipole moment, `overset(to)(m) = q_m ( overset(to) (2l) ) `
The direction of ` overset(to)(m)` is from S to N.
From this equation unit of m is `Am^(2)`.
(Note : The magnetic force acting on a pole of a bar magnet kept in magnetic field of 1 T is known is pole strength).
`therefore q_m = (overset(to) (F_m) )/( overset(to)(B) ) therefore q_m = F_m [ because B = 1T] and overset(to) (F_m) = (q_m) (overset(to) (B) )`
(This equation is similar to static electricity as per `overset(to) (F ) = q (overset(to)(E) )` ).
As electric field by a point charge is `E= (kq)/( r^2)`, similarly magnetic field by a pole of pole strength `q_m` is `B = (mu_0)/( 4pi) (q_m)/( r^2)`.