Laws of Magnetic Force and Permeability

The laws of magnetic force are somewhat similar to Coulomb’s laws of electrostatic force. As per Coulomb’s law, the electrostatic force acts between two opposite or similar charges. In the same way, there is a force acting between two nearby magnetic poles.

Charles Augustin De Coulomb also experimentally determined the expression of force acting between two magnetic poles. So, we can understand that Sir Charles Augustin De Coulomb had expressed both the electrostatic force between two electric charges and magnetic force between two magnetic poles.

charles augustin de coulomb

 

Although, we can create two isolated electrically charged bodies. But we can not create practically two isolated magnetic poles. Because the magnetic poles always exist in pair. That means we can not isolate a north pole from the south pole in a magnet. That is why he took the theoretical way to express the force between two magnetic poles instead of experimentally doing that. However, we can think the round-headed poles of a long and thin bar magnet as the isolated poles.

isolated magnetic poles

Although this is not the ideal isolated poles but he could manage his experiment with this type of considered isolated poles. The measured force between the magnetic poles with a torsion balance. Then he found the following observation.

Statement of Laws of Magnetic Force

  1. The force acting between two magnetic poles is directly proportional to the product of the strengths of magnetic poles.
  2. It is inversely proportional to the square of the distance between the magnetic poles.
  3. Also, the force is inversely proportional to the permeability of the medium in which the poles exist.

Explanation of Laws of Magnetic Force

Suppose, there are two magnetic poles. M1 and M2 represent the magnetic pole strengths of these two poles, respectively. Also, let us assume, r is the distance between the centers of those two magnetic poles. As per laws of  magnetic force,

laws of magnetic force 1

Where μ is the permeability of the medium. Although, we can represent μ as μ0μr

laws of magnetic force 2

Where μ0 is absolute permeability of vacuum or free space. On the other hand is the relative permeability of the medium in which the magnetic poles exist.

Combining the above three relations we get,

laws of magnetic force 3

Here ‘K’ is the constant of proportionality. Sir Charles Augustin De Coulomb had calculated the value of this constant of proportionality in the laws of magnetic force. And he found,

laws of magnetic force 4

Therefore, finally we get the complete equation for the laws of magnetic force,

laws of magnetic force 5

Vector Form of Laws Magnetic Force

Since this is a force, it must have a direction. Hence, it is a vector quantity. And the direction of the force is along the straight line connecting the centers of the poles. The exact direction will be as per the nature of the magnetic poles. Two similar magnetic poles repel each other. Such as two north magnetic poles or two south magnetic poles will repel each other. But two opposite poles attract each other. Such as north magnetic pole attracts south and vice versa. Hence, depending upon the nature of poles we get the direction of the force acting between them. Vectorically, we can represent the force as,

 

Unit of Magnetic Pole

If we put, M1=M2=Mlaws of magnetic force 7

Then,laws of magnetic force 8

Now, if M is 1 unit, we can write,laws of magnetic force 9

Again, if we consider that the surrounding is a vacuum, the relative permeability (μr) is 1. Therefore,laws of magnetic force 10

We have already considered M as a unit pole strength. So, we can define the unit pole strengths or the unit magnetic poles are such poles which repel or attract each other with the force of laws of magnetic force 11

The unit pole strength is expressed in weber.

Concept of Absolute and Relative Permeability

In the laws of magnetic force, we have found that the force between two magnetic poles depends on the permeability of the medium in which poles exist. Absolute permeability means the actual permeability. The permeability of vacuum is 4π×10-7H/m. The relative permeability is the ratio of the permeability of a certain medium to the absolute permeability of vacuum or free space. Therefore we can write,laws of magnetic force 12

The relative permeability of a medium is 10. Hence the absolute or practical permeability islaws of magnetic force 13

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