The SI unit of permittivity of free space (ϵ0 ) is

Explanation

The SI unit of permittivity of free space (ϵ0 ) is (d) C^2/Nm².It is a measure of a material's ability to permit the flow of electric field lines. Let's break down how this unit arises:Coulomb (C): This unit represents the amount of electric charge.Newton (N): This unit represents force.Meter (m): This unit represents distance.Permittivity (ε₀): This quantity relates the electric field (E) to the electric displacement field (D) through the equation:D = ε₀ * EThe electric displacement field (D) is another way to describe the electric field, taking into account the medium the field is present in. In free space (a vacuum), D and E are directly proportional with a constant of proportionality equal to ε₀.Deriving the unit:From the equation D = ε₀ * E, we can see that:D has units of C/m² (charge per unit area).E has units of N/C (force per unit charge).Solving for ε₀:ε₀ = D / E = (C/m²) / (N/C)Performing the division, we get:ε₀ = C² / (N m²)Incorrect options: (a), (b), and (c) These units do not correctly represent the SI unit of permittivity of free space.