The figure below shows a plane electromagnetic sinusoidal wave propagating in the $x$ direction. Suppose the wavelength is $46\mathrm{.}0$ m and the electric field vibrates in the $xy$ plane with an amplitude of $26\mathrm{.}0\frac{V}{m}.$

$($i$)$

$($a$)$ Calculate the frequency of the wave.

$MHz$

$($b$)$ Calculate the magnetic field vec$(B)$ when the electric field has its maximum value in the negative $y$ direction.

magnitud$$ :

direction $$

$($c$)$ Write an expression for vec$(B)$ with the correct unit vector, with numerical values for $B_{\text{m}\text{a}\text{x}},k,$ and $,$ and with its magnitude in the form

$B=B_{\text{m}\text{a}\text{x}}cos(kx-t).$

$($Assume $B$ is measured in $nT,x$ is measured in m and $t$ in s $.)$

vec$(B)=-,cos[,x-(,{10}^7)t]hat(k)nT$