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Answer: The Unit of magnetic pole strength in the M.K.S. system is ampere-metre (A·m). In the M.K.S. (Metre-Kilogram-Second) system, magnetic pole strength (denoted as mmm) is the measure of the strength of a magnetic pole, and its unit is derived from the force between magnetic poles. Based on Coulomb’s law for magnetism, the force between two magnetic poles is proportional to the product of their strengths and inversely proportional to the square of the distance between them.
Complete Answer:
We can derive the unit of magnetic pole strength by considering the force experienced by a magnetic pole in a magnetic field. The magnetic field (B) exerts a force (F) on a magnetic pole of strength (m) given by:
F = mB
From this, we can express the magnetic pole strength as:
m = F/B
Now, let’s consider the unit of magnetic field (B). One way to define the magnetic field is through the force it exerts on a moving charge (q) with velocity (v), known as the Lorentz force:
F = q(v×B)
The magnitude of this force is F = qvBsinθ, where θ is the angle between the velocity and the magnetic field. If the velocity is perpendicular to the magnetic field (sinθ=1), then F = qvB.
From this, the unit of magnetic field (B) can be expressed as:
[B] = [F] / [q][v]= Newton / (Coulomb⋅metre/second) = N⋅s / C⋅m
We know that electric current (I) is the rate of flow of charge (I = q/t), so Coulomb (C) can be written as Ampere (A) × second (s), i.e., [C] = [A⋅s]. Substituting this into the unit of magnetic field:
[B] = N⋅s / (A⋅s)⋅m = Newton / (Ampere⋅metre)
Now, substituting the unit of force (Newton) and the derived unit of magnetic field into the equation for the unit of magnetic pole strength:
= [m] = [F] / [B]
= {Newton / (Newton / (Ampere⋅metre))}
= Newton × {Ampere⋅metre / Newton}
= Ampere⋅metre
Therefore, the unit of magnetic pole strength in the M.K.S. system is Ampere-metre (Am).
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