Question

The magnetic field amplitude of an electromagnetic wave is $ 2\times {{10}^{-7}}T $ , Its electric field amplitude, if the wave is travelling in free space is:

• A. $ 6\,\,V{{m}^{-1}} $
• B. $ 60\,\,V{{m}^{-1}} $
• C. $ \frac{1}{6}\,V{{m}^{-1}} $
• D. none of these

Answer 1

Answer: (B)

We can write the electric and magnetic fields as sinusoidal functions of position $x$ and time $t$.
$E=E_{0} \sin (k x-\omega t) $
$B=B_{0} \sin (k x-\omega t)$
In this $E_{0}$ and $B_{0}$ are the amplitudes of the fields. Further
$c =\frac{E_{0}}{B_{0}}$
$E_{0} =B_{0} c$
Given, $B_{0}=2 \times 10^{-7} T$,
$ c =3 \times 10^{8} \,m / s$
we have
$E_{0}=2 \times 10^{-7} \times 3 \times 10^{8}$
$=60\, Vm ^{-1}$