A plane EM wave is propagating along $$x$$ direction. It has a wavelength of $$4$$ mm. If electric field is in $$y$$ direction with the maximum magnitude of $$60$$ Vm$$^{-1}$$, the equation for magnetic field is :

An EM wave propagating along x-direction with electric field in y-direction.

$$\lambda = 4$$ mm = $$4 \times 10^{-3}$$ m, $$E_0 = 60$$ V/m.

The magnetic field is perpendicular to both propagation direction (x) and electric field (y), so it is along the z-direction.

Magnitude of magnetic field: $$B_0 = \frac{E_0}{c} = \frac{60}{3 \times 10^8} = 2 \times 10^{-7}$$ T.

Wave number: $$k = \frac{2\pi}{\lambda} = \frac{2\pi}{4 \times 10^{-3}} = \frac{\pi}{2} \times 10^3$$ m$$^{-1}$$.

The magnetic field equation is:

$$B_z = 2 \times 10^{-7} \sin\left[\frac{\pi}{2} \times 10^3(x - 3 \times 10^8 t)\right] \hat{k} \text{ T}$$

The correct answer is Option 1.