Current Loop as AMagnetic Dipole and its Magnetic Dipole Moment
Magnetic Dipole
When two opposing and equal magnetic poles are separated by a small distance then it is said to be magnetic dipole. Whereas the magnetic dipole moment of the magnetic dipole can be defined as strength as the pole and magnetic length, the magnetic dipole moment is a vector quantity and it is directed from S pole to N pole. The electrons are always circulating around nuclei of atoms, and these electrons are continuously spinning on their axis and the rotation of positively charged atomic nuclei all are magnetic dipoles. The sum of the effects can be canceled so the given type of atoms may not be the magnetic dipoles, But if the effects are not fully canceled then the atom acts like a permanent magnetic dipole. This behavior is mostly observed in the atoms of iron. Spontaneously, millions of iron atoms are locked into the same alignment to make the ferromagnetic domain that is constituent of a magnetic dipole.
It was found by Ampere that the distribution of magnetic lines of forces around the finite solenoid that is carrying current is similar to that which is produced by a bar magnet. At a point, the magnetic induction, along the axis of the circular coil that is carrying current can be expressed by the following formula.
The direction of the magnetic field is given by right-hand rule and it is along the axis. If the points are far away from the center of the coil then for such points the situation is as follows.
Now, let consider a circular loop, if n=1 then its area A=πa2
Here the magnetic induction at a point along the line of axis of short bar magnet is
So, the current loop is equivalent to the magnetic dipole of the moment. Generally, the magnetic dipole is a tiny magnet of a microscope to the subatomic dimensions and is equivalent to the flowing electric charges around the loop. The magnetic dipole moment can be considered as a measurement of the ability of dipoles for turning itself into alignment with the given amount of external magnetic field. When the magnetic field is uniform, then the magnitude of the dipole moment is proportional to maximum torque. Simply the magnetic dipole moment is also known as a magnetic moment.
For consideration of magnetic dipole as a current loop, the magnitude of dipole moment is proportional to current multiplied by the size of the enclosed area. The dimensions of magnetic dipole moments are the same as that of current times area or the energy divided by magnetic flux density. Its SI unit is ampere square meter.