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.

Question

Using the formulae show that the S.I. units of the magnetic field B and the permeability constant μ 0 may be written as N mA –1 and NA –2 respectively.

Philoid · Accepted Answer

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.

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.

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.