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Asked by mauryaprapti9 | 28 May, 2024, 10:33: AM

Dimensions of each quantity should be expressed in terms of dimesions of fundamental quantities like

length(L) , mass (M), Time (T), Ampere (A)

units of charge e  :- C = A s

units of permittivity of free space, εo = F/m  = C/(V m )

1 volt = 1 J/ C

units of εo = C2 / ( J m ) = ( A2 s2 ) / ( kg m s-2 m2 ) = A2 s4 kg-1 m-3

units of planck constant , h = J s = kg m2 s-1

units of speed of light c = m/s

------------------------------------

If  the combination of  eα εoβ hγ cδ  is dimensionless , then we get

[ A T ]α [ A2 T4 M-1 L-3 ]β [ M L2 T-1 ]γ [ L T-1 ]δ  = Ao To Mo Lo

By equating exponents of same dimension on both sides

α + 2 β = 0

α + 4 β - γ - δ = 0

-β + γ = 0

-3β + 2γ + δ = 0

By solving above equations , we get

if α = 2 , then β = γ = δ = -1

Answered by Thiyagarajan K | 28 May, 2024, 03:16: PM

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