Q 12-08-052JEE MainJEE Main 2024 (4 Apr, Shift 1)Easy
The electric field in an electromagnetic wave is given by $\vec E = \hat i\,40\cos\omega(t - z/c)\ \text{N C}^{-1}$. The magnetic field induction of this wave is (in SI units)
Answer: (D) $\vec B = \hat j\dfrac{40}{c}\cos\omega(t - z/c)$
The wave travels along $+z$ and $\vec E$ is along $\hat i$. Since $\vec E\times\vec B$ must point along $+\hat k$ and $\hat i\times\hat j = \hat k$, $\vec B$ is along $\hat j$ with $B_0 = \dfrac{E_0}{c} = \dfrac{40}{c}$:
$$\vec B = \hat j\frac{40}{c}\cos\omega(t - z/c)$$
Solution by Sreeraj P, M.Sc Physics