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Asked in GUJCET 2018 · Units and dimensions
Given: the product μ₀ε₀.
Idea: the speed of light in vacuum is c=1/(√μ₀ε₀), so μ₀ε₀=1/(c²).
[c]=L¹T⁻¹, so [c²]=L²T⁻² and [μ₀ε₀]=M⁰L⁻²T².
Check from the constants themselves: [μ₀]=M¹L¹T⁻²A⁻² and [ε₀]=M⁻¹L⁻³T⁴A², whose product is M⁰L⁻²T² -- the current dimension cancels too.
So μ₀ε₀ has the dimensions M⁰L⁻²T², the reciprocal of a speed squared.
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