Question 144: EM waves

Question

A plane electromagnetic wave of wavelength $$\lambda $$ has an intensity I.  It is propagatting along the positive Y-direction. The allowed expressions for the electric and magnetic fields are givn by :

Accepted Answer

$$\overrightarrow E $$ is electric field vector, $$\overrightarrow B $$ is magnetic field vector perpendicular to $$\overrightarrow E $$. The direction of propagation is $$(\overrightarrow E  	imes \overrightarrow B )$$. The direction of propagation of wave is along + y axis, then $$\overrightarrow E $$ is along + z axis and $$\overrightarrow B $$ is along + x axis.
$$(E\widehat k 	imes B\widehat i) = EB(\widehat k 	imes \widehat i) = EB\widehat j$$
As wave is travelling along + y axis with time, we will use (y $$-$$ ct) in wave equation.
Also, intensity is given by
$$I = {1 \over 2}c{\varepsilon _0}E_0^2$$
And $$E = cB$$
So, $$|{E_0}| = \sqrt {{{2I} \over {c{\varepsilon _0}}}} $$
Therefore, $$\overrightarrow E  = \sqrt {{{2I} \over {c{\varepsilon _0}}}} \cos \left[ {{{2\pi } \over \lambda }(y - ct)} ight]\widehat k$$
And $$\overrightarrow B  = {E \over c}\widehat i \Rightarrow {1 \over c}E\widehat i$$

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EM waves

A plane electromagnetic wave of wavelength $\lambda $ has an intensity I. It is propagatting along the positive Y-direction. The allowed expressions for the electric and magnetic fields are givn by :

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