Electromagnetic waves > Properties of emission and reflection of electromagnetic waves > Problem 12.1.6

Statement

$12.1.6.$ An electromagnetic wave occupies the space between two parallel infinite planes $AB$ and $A'B'$. The illustrated segment of the electromagnetic field moves at the speed of light $c$ in a direction perpendicular to the plane $AB$. The electric field strength of the wave is $E$. By applying the law of electromagnetic induction to the rectangular loop (contour) $baa'b'$, determine the magnetic induction of the wave in SI and CGS units.

Solution

Let $ab=L$.By applying the law of electromagnetic induction to the countour $baa'b'$ we get:

\begin{equation}
E L=\frac{d\Phi}{dt}
\end{equation}

In time $dt$ the wave moves a distance $cdt$.So the change of the magnetic flux is:

\begin{equation}
d\Phi=BLcdt
\end{equation}

By plugging eq(2) into the first we find that(in SI units):

\begin{equation}
B=\frac{E}{c}
\end{equation}

In Gaussian units Faraday's law for the same countour looks like:

\begin{equation}
EL=\frac{1}{c}\frac{d\Phi}{dt}
\end{equation}

So the answer in CGS units is:

\begin{equation}
B=E
\end{equation}

Answer

$B=\frac{E}{c}$(in SI) $B=E$(in CGS)