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Asked in GUJCET 2019 · Units and dimensions
Given: relative permittivity εᵣ and relative permeability μᵣ.
Idea: each is defined as a ratio of two quantities of the same kind -- εᵣ=ε/(ε₀) and μᵣ=μ/(μ₀).
In such a ratio every unit cancels, so each factor is a pure number, and so is their product.
So [εᵣμᵣ]=M⁰L⁰T⁰A⁰ -- the quantity is dimensionless.
As a check on the physics: εᵣμᵣ=(c²)/(v²), the square of the refractive index of the medium, which is also a pure number.
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