If ₀ , e and h represent the permeability of free space, elementary charge and Planck's constant respectively, then the dimensional formula of ₀ e^2 h is :

Step-by-step solution

First, write the dimensional formulas for each physical quantity: Permeability of free space ( ₀ ): From the force per unit length between parallel currents F L = ₀ I₁ I₂ 2 r , we get [ ₀] = [ M L T ⁻²][ L ] [ L ][ A ^2] = [ M L T ⁻² A ⁻²] Elementary charge ( e ): From q = It , [e] = [ A T ] Planck's constant ( h ): From E = h , [h] = [ M L ^2 T ⁻²] [ T ⁻¹] = [ M L ^2 T ⁻¹] Now, substitute these into the given expression ₀ e^2 h : [ ₀ e^2 h ] = [ M L T ⁻² A ⁻²] [ A T ]^2 [ M L ^2 T ⁻¹] [ ₀ e^2 h ] = [ M L T ⁻² A ⁻²