# Using the formulae show that the S.I. units of the magnetic field B and the permeability constant μ0 may be written as N mA–1 and NA–2 respectively.

Given:  Formula used:
Lorentz force: Where, is the magnetic force vector, q is the charge, is the velocity vector and is the magnetic field vector.

Magnetic field can be written as: Unit of force is Newton: N
Charge: q = It
Unit of current : I = Amperes= A
Unit of time : t = seconds = s
Unit of charge : q = As
Unit of velocity : v = m/s
Thus, unit of Magnetic field:  Therefore, unit of Magnetic field : B = N m-1A-1.
Now,
Ampere’s Law: Where,

μ0 is the permeability of free space,

I is the current flowing

r is the radius of the current carrying wire.
SI Unit of B = N mA-1
SI Unit of I = A
SI Unit of r = m   Thus, unit of permeability constant μ0 is N A-2.
Hence proved that unit of Magnetic field is N m-1A-1 and unit of permeability constant μ0 is N A-2.

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