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The dimension of 1/(με) is the same as the dimension of ________, where μ is the magnetic constant and ε the permittivity.

Asked in GSEB Board March 2020 · Units and dimensions

Answer: (2) Square of velocity

Step-by-step solution

Given: 1/(με), with μ the permeability and ε the permittivity of the medium.

Idea: the speed of an electromagnetic wave in a medium is v=1/(√με).

Squaring both sides, v²=1/(με).

Check it from the constants: [μ]=M¹L¹T⁻²A⁻² and [ε]=M⁻¹L⁻³T⁴A², so [με]=M⁰L⁻²T² and its reciprocal is M⁰L²T⁻².

M⁰L²T⁻² is (L¹T⁻¹)², so the answer is the square of velocity.

Why the other options are wrong

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