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 μ 0 can be expressed in units of:

Step-by-step solution

Magnetic potential energy inside a solenoid is U = 1 2 L I 2 Where L = self-inductor ⇒ U = 1 2 μ 0 n 2 A   l I 2 ∵ n = number of turns per unit length = N l U = 1 2 μ 0 N l 2 A l   I 2 U = 1 2 μ 0 N 2 l 2 A l   I 2   μ 0 = 2 U l N 2 A I 2 Dimensionally, U = h c λ I = e T A = l 2 l = l ′ μ 0 = h c λ   [ l ] l 2 t 2 e 2 = h λ t e 2 = h c e 2 μ 0 = h c e 2