Question

Using the formula $\overrightarrow{F}=\overrightarrow{qv}\times \overrightarrow{B}$ and $B=\frac{{\mu }_{0}i}{2\pi r}$ , show that the SI units of the magnetic field B and the permeability constant ${\mu }_0$ may be written as $Nm{A}^{-1}$ and $N{A}^{-2}$ respectively.

Answer 1

Given $\overrightarrow{F}=a\overrightarrow{v}\times \overrightarrow{B}$

That gives $B=\frac{F}{qv}+\frac{F}{Itv}=N/A-m$

Again, $B=\frac{{\mu }_{0}i}{2\pi r}$

$\Rightarrow {\mu }_0=B,\frac{2\pi r}{i}=\frac{N}{A-m},\frac{m}{A}$