Question

Which of the following relations is correct with regards to electric and magnetic field oscillation vector in case of $EM$ waves (wave is propagating in the $x$ direction)?

• A. $\frac{\partial E}{\partial x}=\frac{\partial B}{\partial t}$
• B. $\frac{\partial E}{\partial x}=-\frac{\partial B}{\partial t}$
• C. $\frac{\partial E}{\partial t}=\frac{\partial B}{\partial x}{\mu }_0{\epsilon }_0$
• D. $\frac{\partial E}{\partial t}=-\frac{\partial B}{\partial x}{\mu }_0{\epsilon }_0$

Answer 1

The correct option is B $\frac{\partial E}{\partial x}=-\frac{\partial B}{\partial t}$

We know that, $\oint \overrightarrow{E}.\overrightarrow{dl}=-\frac{d{\varphi }_B}{dt}$


Considering a small part of $EM$ wave as shown in the figure,

$(E+d\overline{E})h-hE=-hdx\frac{\partial B}{\partial t}$

$\Rightarrow \frac{\partial E}{\partial x}=-\frac{\partial B}{\partial t}$

Hence, option $\left(b\right)$ is correct.