Permeability of Free Space (µ0) Dimension Calculation Magnetic field intensity in at a point in space due to an infinitely long current carrying conducting wire B=‌
µ0I
2Ï€r
⇒µ0=‌
2Ï€rB
I
....(i) Now, the magnetic force experienced by a current carrying conductor, when placed in a uniform external magnetic field is given by F=ILB‌sin(θ)⇒B=‌
F
IL‌sin(θ)
Put this value of B into Eq. (ii) to get µ0=‌
2Ï€r[
F
IL‌sin(θ)
]
I
=‌
2Ï€rF
I2L‌sin(θ)
⇒‌‌[µ0]=‌
[2Ï€][r][F]
[I2][L][sin(θ)]
=‌
[M0L0T0][L1][M1L1T−2]
[A2][L1][M0L0T0]
=[M1L1T−2A−2]....(iii) So, now [‌
E2
µ0
]=‌
[E]2
[µ0]
On putting the values from Eqs. (i) and (iii), we will get