An EM wave propagating in x -direction has a wavelength of 8mm ....

An EM wave propagating in

x

-direction has a wavelength of

8mm

. The electric field vibrating

y

-direction has maximum magnitude of

60{Vm}^{- 1}

. Choose the correct equations for electric and magnetic fields if the EM wave is propagating in vacuum :

Options

A
${E}_{y} = 60\sin \left[\dfrac{\pi}{4} \times {10}^{3}\left(x - 3 \times {10}^{8}t\right)\right]\overset{^}{j}V{m}^{- 1}$
${B}_{z} = 2\sin \left[\dfrac{\pi}{4} \times {10}^{3}\left(x - 3 \times {10}^{8}t\right)\right]\overset{^}{k}T$
B
${E}_{y} = 60\sin \left[\dfrac{\pi}{4} \times {10}^{3}\left(x - 3 \times {10}^{8}t\right)\right]\overset{^}{j}V{m}^{- 1}$
${B}_{z} = 2 \times {10}^{- 7}\sin \left[\dfrac{\pi}{4} \times {10}^{3}\left(x - 3 \times {10}^{8}t\right)\right]\overset{^}{k}T$
C
${E}_{y} = 2 \times {10}^{- 7}\sin \left[\dfrac{\pi}{4} \times {10}^{3}\left(x - 3 \times {10}^{8}t\right)\right]\overset{^}{j}V{m}^{- 1}$
${B}_{z} = 60\sin \left[\dfrac{\pi}{4} \times {10}^{3}\left(x - 3 \times {10}^{8}t\right)\right]\overset{^}{k}T$
D
${E}_{y} = 2 \times {10}^{- 7}\sin \left[\dfrac{\pi}{4} \times {10}^{4}\left(x - 4 \times {10}^{8}t\right)\right]\overset{^}{j}V{m}^{- 1}$
${B}_{z} = 60\sin \left[\dfrac{\pi}{4} \times {10}^{4}\left(x - 4 \times {10}^{8}t\right)\right]\overset{^}{k}T$

${E}_{y} = 60\sin \left[\dfrac{\pi}{4} \times {10}^{3}\left(x - 3 \times {10}^{8}t\right)\right]\overset{^}{j}V{m}^{- 1}$

${B}_{z} = 2 \times {10}^{- 7}\sin \left[\dfrac{\pi}{4} \times {10}^{3}\left(x - 3 \times {10}^{8}t\right)\right]\overset{^}{k}T$

Using the relation $\overset{\to}{E} = c\overset{\to}{B}$ , where, $c$ is speed of light in vacuum.

After analysing each option, we get option $B$ is the correct option

as $\overset{\to}{E}\overset{\to}{B} = \dfrac{60}{2 \times {10}^{- 7}} = 3 \times {10}^{8}m{s}^{- 1}$ .