1. Given electric field

   $\vec E = E_0 \cos(\omega t-kz)\,\hat i$

2. Direction of propagation

   A wave of the form $\cos(\omega t-kz)$ propagates in the positive $z$-direction.

3. Direction of magnetic field

   For an electromagnetic wave, $\vec E \perp \vec B \perp \text{direction of propagation}$ and $\vec E \times \vec B$ gives the direction of propagation.

   Here:

   • $\vec E$ is along $\hat i$
   • propagation is along $\hat k$

   So we need $\hat i \times \vec B = \hat k$.

   Since $\hat i \times \hat j = \hat k,$ the magnetic field must be along $\hat j$.

4. Magnitude relation

   In free space, $E_0 = cB_0 \quad \Rightarrow \quad B_0 = \frac{E_0}{c}$

5. Phase relation

   In an electromagnetic wave in free space, $\vec E$ and $\vec B$ are in phase. Therefore $\vec B$ must have the same phase factor:

   $\cos(\omega t-kz)$

6. Hence

   $\boxed{\vec B = \frac{E_0}{c}\cos(\omega t-kz)\,\hat j}$

7. Option check

   • A: wrong magnitude and wrong phase
   • B: correct
   • C: wrong magnitude
   • D: wrong phase

Therefore, the correct option is B.