The plot below depicts the electric field component of a linearly polarized, electromagnetic plane wave traveling through vacuum. $E(r,t)$ propagates in the negative z$-$direction and toward an observer located at $z=0.($Note that $x$ is directed into the page.$)$

What is the magnetic field associated with this wave $($assuming $k$ and $$ have their usual definitions$)?$

$($a$)B(r,t)=x{B}_{\text{m}\text{a}\text{x}}sin(kz-t)$

$($b$)B(r,t)=x{B}_{\text{m}\text{a}\text{x}}sin(kz+t)$

$($c$)B(r,t)=z{B}_{\text{m}\text{a}\text{x}}sin(kz-t)$

$($d$)B(r,t)=-x{B}_{\text{m}\text{a}\text{x}}sin(kz+t)$

$($e$)B(r,t)=-x{B}_{\text{m}\text{a}\text{x}}sin(kz-t)$