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.
For problem $12.1.6$
Solution
Let $ab = L$. By applying Faraday's law of electromagnetic induction to the contour $baa'b'$ we get: $$EL = \frac{d\Phi}{dt}$$
In time $dt$, the wave moves a distance $c dt$. So the change of the magnetic flux is: $$d\Phi = B L c dt$$
By plugging the second equation into the first, we find the induction in SI units: $$EL = B L c \implies B = \frac{E}{c}$$
In Gaussian units (CGS), Faraday's law for the same contour looks like: $$EL = \frac{1}{c} \frac{d\Phi}{dt}$$
Substituting the flux expression, the answer in CGS units is: $$EL = \frac{1}{c} B L c \implies B = E$$
