Answer:
If the period of the wave is increased by the factor of 2.70, the wavelength of the wave is also increased by a factor of 2.70. So,
[tex]\lambda_2 = 235\times 2.70 = 634.5 ~nm[/tex]
The magnetic field component can be written as
[tex]\vec{B} = \frac{E_{max}}{c}e^{i(\vec{k}\vec{z}-\omega t)}\^{z}[/tex]
The magnetic field is in the z-direction, because the E-field is directed towards +y and the wave is propagating in the +x-direction. The right-hand rule gives us the direction of the B-field.
[tex]\vec{E} \times \vec{B} = \vec{S}[/tex]
S is the Poynting vector which gives us the propagation of the wave.
We will use the following relationships
[tex]k = 2\pi / \lambda\\f = \omega / 2\pi\\c = \lambda f = \lambda \omega / 2\pi\\\omega = 2\pi c/\lambda[/tex]
[tex]\vec{B} = \frac{7.7\times 10^{-3}}{3\times 10^8}e^{(\frac{2\pi}{3\times 10^8}z - \frac{2\pi\times 3\times 10^8}{634.5})}\\\vec{B} = 2.56\times10^{-11} e^{(2.09\times10^{-8}z - 2.96\times10^{6}t)}\^{z}[/tex]
