Question

The formula for the velocity of electromagnetic waves in vacuum is given by

• A. $c=\sqrt{{\mu }_0\epsilon }$
• B. $c=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}$
• C. $c=\sqrt{\frac{{\mu }_0}{{\epsilon }_0}}$
• D. $c=\sqrt{\frac{{\epsilon }_0}{{\mu }_0}}$

Answer 1

The correct option is B $c=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}$

Maxwell deduced that the speed of propagation of an electromagnetic wave through a vacuum is entirely determined by the constants ${\mu }_0$ and ${ϵ}_0$ as the following:
$c=\frac{1}{\sqrt{{\mu }_0{ϵ}_0}}$
We know that ${\mu }_0=4\pi \times {10}^{-7}N{s}^2{C}^{-2}$ and ${ϵ}_0=8.854\times {10}^{-12}{C}^2{N}^{-1}{m}^{-2}$ which gives:
$c=\frac{1}{\sqrt{4\pi \times {10}^{-7}8.854\times {10}^{-12}}}=2.998\times {10}^8$ m/s