Question

Show that, when SI units for μ0 and ϵ0 are entered, the units given by the right-hand side of the equation in the problem above are m/s.

Answer 1

We know that

$c=\frac{1}{\sqrt{\mu_0\epsilon_0}}\rightarrow(1)$

RHS

Unit of

$\mu_0=\frac{T\times m}{A}$

$\epsilon=\frac{c^2}{N\times m^2}$

$A=\frac{c}{sec}$

$\mu_0=\frac{T\times sec\times m}{c}$

Equation (1) put RHS value

$c=\frac{1}{\sqrt{\frac{T\times m \times sec}{c} \times{\frac {c^2}{N\times m^2}}}}$

$c=\frac{1}{\sqrt{\frac{T \times sec\times c}{N\times m}}}\rightarrow(2)$

Now We know that

$F=qvB$

$v=\frac{F}{qB}$

Unit

$v=\frac{N}{c\times T}\rightarrow({3})$

Equation (2) and (3) we can written as

$c=\frac{1}{\sqrt{\frac{1}{v}\times \frac{sec}{m}}}$

$\frac{1}{v}=\frac{sec}{m}$

$c=\frac{1}{\sqrt{\frac{1}{v^2}}}$

$c=v$

Unit of c=v =m/sec

LHS=RHS