Q 12-08-220JEE MainJEE Main 2019 (12 Apr, Shift 2)Medium
A plane electromagnetic wave having a frequency $f = 23.9$ GHz propagates along the positive $z$-direction in free space. The peak value of the electric field is $60$ V/m. Which among the following is the acceptable magnetic field component in the electromagnetic wave?
Answer: (A) $\vec{B} = 2\times10^{-7}\sin\left(0.5\times10^3z - 1.5\times10^{11}t\right)\hat{i}$
$B_0 = \dfrac{E_0}{c} = \dfrac{60}{3\times10^8} = 2\times10^{-7}$ T.
$\omega = 2\pi f \approx 1.5\times10^{11}$ rad/s and $k = \dfrac\omega c \approx 0.5\times10^3$ m$^{-1}$.
For travel along $+z$ the phase must be $(kz - \omega t)$, and $\vec{B}$ must be perpendicular to $z$. Only option (1) satisfies all of these.
Solution by Sreeraj P, M.Sc Physics