Question

The dimensional formula of permeability and permittivity is

Answer 1

$Permittivity$

[M^ -1 l^ -3 T^4 A^2]

$Permeability$

[MLT^-2*A^-2]

Hope it helps you.

Answer 2

(1) We know B = μ H

So μ = B/H

Unit of H is Ampere/meter (A/m)

Unit of B is Newton per Amp meter (N/A.m)

Unit of μ is Newton per Amp² (N/A²)

Newton i.e. Force has dimension [ML$T^{-2}$]

So dimension of μ is [MLT$T^{-2}A^{-2}$]

(2) As per Coulomb's Law,

F = $\frac{q_{1}.q_{2} }{4\pi.∈ r^{2}}$

∈ = $\frac{q_{1}.q_{2} }{4\pi.F r^{2}}$ ....(i)

We know the dimensions of

F = [ML$T^{-2}$]

r = [L]

q = [TA]

Putting in (i) we get

dimension of permittivity ∈ as [$M^{-1} . L^{-3}. T^{4}. A^{2}$]