Question

What is the $SI$ unit of permeability?

• A. henry per metre
• B. tesla metre per ampere
• C. weber per ampere metre
• D. All of these.

Answer 1

Answer: (D)

$L_{\text{solenoid }}=\frac{{\mu }_0{N}^{2}A}{l},$ where $N$ is the number of turns
$\Rightarrow \left[{\mu }_0\right]=\frac{[L][l]}{\left[N^2\right][A]}=\frac{\text{ henry }\cdot m}{m^2}$
$\left[{\mu }_0\right]=$ henry per metre.
Also, $B_{\text{solenoid }}=\frac{{\mu }_{0}NI}{l}$
$\left[{\mu }_0\right]=\frac{[B][l]}{[N][I]}=$ tesla metre per ampere.
Also, $\varphi =BA\Rightarrow$ weber $=$ tesla metre ${}^2$
$Wb=T{m}^2$
As $\left[{\mu }_0\right]=Tm{A}^{-1}=Wb{m}^{-1}{A}^{-1}=$ Weber per (ampere
metre).