The quantity (1 / 2)ε₀E² represents the energy density of an electric field, where ε₀ is the permittivity of free space and E is the electric-field magnitude. If its dimensional formula is written as MᵃLᵇTᶜ, what is the value of 2a-b+c?
Options

Question

The quantity (1 / 2)ε₀E² represents the energy density of an electric field, where ε₀ is the permittivity of free space and E is the electric-field magnitude. If its dimensional formula is written as MᵃLᵇTᶜ, what is the value of 2a-b+c?

Options

G1 Physics · Accepted Answer

The quantity (1 ÷ 2)ε₀E² is electric-field energy density. Energy density has dimensions [energy] ÷ [volume]. Therefore, [(1 ÷ 2)ε₀E²] = [M L² T⁻²] ÷ [L³] = [M L⁻¹ T⁻²]. Hence, a = 1, b = -1, c = -2. Therefore, 2a-b+c = 2(1)-(-1)+(-2) = 2+1-2 = 1. Correct option: B.