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If electronic charge e, electron mass m, speed of light in vacuum c and Planck's constant h are taken as fundamental quantities, the permeability of vacuum μ₀ can be expressed in units of

Asked in JEE Main Online 2015 · Expressing a quantity in new base units

Answer: (3) (h/(ce²))

Step-by-step solution

Given: μ₀=[MLT⁻²A⁻²], with e=[TA], c=[LT⁻¹], h=[ML²T⁻¹].

Test h/(ce²):

Denominator: [LT⁻¹][T²A²]=[LTA²].

([ML²T⁻¹])/([LTA²])=[MLT⁻²A⁻²].

That is exactly the permeability, so μ₀ is measured in units of h/(ce²).

Why the other options are wrong

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