A plane electromagnetic wave of wavelength $\lambda$ has an intensity $I$. It is propagating along the positive $Y$-direction. The allowed expressions for the electric and magnetic fields are given by:
Answer: (A) $\vec E = \sqrt{\dfrac{2I}{\varepsilon_0c}}\cos\left[\dfrac{2\pi}{\lambda}(y - ct)\right]\hat k,\quad \vec B = +\dfrac1cE\,\hat i$
- **Amplitude:** $I = \dfrac12\varepsilon_0cE_0^2$, so $E_0 = \sqrt{\dfrac{2I}{\varepsilon_0c}}$. This rules out options (2) and (4).
- **Direction of travel:** $(y - ct)$ describes a wave moving along $+y$, which rules out option (3).
- **Field directions:** $\vec E\times\vec B$ must point along $+\hat j$. With $\vec E$ along $\hat k$ and $\vec B$ along $\hat i$, $\hat k\times\hat i = \hat j$. ✓
Option (1) is correct.
Solution by Sreeraj P, M.Sc Physics