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Question

Physics Question on Dimensional Analysis

The dimensional formula of permeability of free space μ0\mu_0 is

A

[MLT2A2][MLT^{-2}A^{-2}]

B

[M0L1T][M^0 L^1 T]

C

[M0L2T1A2][M^0 L^2 T^{-1}A^2]

D

none of these

Answer

[MLT2A2][MLT^{-2}A^{-2}]

Explanation

Solution

Permeability of free space
μ0=2π×force×distancecurrent×current×length\mu_0=\frac{2\pi \times \, force \, \times \, distance}{current \, \times \, current \, \times \, length}
Dimensional formula of μ0=[MLT2][L][A][A][L]\mu_0=\frac{[MLT^{-2}][L]}{[A][A][L]}
=[MLT2A2]=[MLT^{-2}A^{-2}]