Question

In SI units, the dimensions of `sqrt((ε_0)/(mu_0))` is ______.

Options

• [A^-1TML³]

• [AT²M^-1L^-1]

• [AT^-3ML^3/2]

• [A²T³M^-1L^-2]

Answer 1

In SI units, the dimensions of `sqrt((ε_0)/(mu_0))` is [A²T³M^-1L^-2].

Explanation:

Given: `sqrt((ε_0)/(mu_0))`

To find: SI unit dimension of `sqrt((ε_0)/(mu_0)`.

Unit of Free Space Permittivity, `ε_0 = c^2/(m^2N)`; (through Coulomb's law),

To obtain the dimensional formula [ε₀] = [M^-1L^-3T⁴A²], reduce the unit.

[ε₀] = [M^-1L^-3T⁴A²] ......(i)

Also, `sqrt((ε_0)/(mu_0)) = sqrt((ε_0^2)/(ε_0mu_0))` = cε₀ ....(ii) `("as", c = 1/sqrt(ε_0mu_0))`

The dimensions of `sqrt((ε_0)/(mu_0)")` will be dimensions of c times dimensions of ε₀ from (i) and (ii):

`sqrt((ε_0)/(mu_0)) = [c][ε_0]`

= [L¹T^-1][M^-1L^-3T⁴A²]

= [M^-1L^-2T³A²]