In a specific unit system, a magnetic field's dimensions can be represented using the electric charge e, the mass of an electron mₑ, Planck's constant h, and Coulomb's constant k = 1 / (4πϵ₀), where ϵ₀ represents the vacuum permittivity. If the dimensions of the magnetic field [B] are expr

Question

In a specific unit system, a magnetic field's dimensions can be represented using the electric charge e, the mass of an electron mₑ, Planck's constant h, and Coulomb's constant k = 1 / (4πϵ₀), where ϵ₀ represents the vacuum permittivity. If the dimensions of the magnetic field [B] are expressed as [e]ᵅ [mₑ]ᵝ [h]ᵞ [k]ᵟ, what is the sum of the exponents α, β, γ, and δ?

Accepted Answer

4. The dimensional analysis of the magnetic field [B] in terms of e, mₑ, h, and k gives the exponents α = 1, β = 1, γ = 1, and δ = 1. Adding these exponents gives a total sum of 4.

Solution

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