1. Given magnetic field

   $\vec B = B_0 \sin(kx+\omega t)\,\hat j$

   So, the magnetic field is along the $+y$-direction.

2. Determine the direction of propagation

   A wave of the form

   $\sin(kx-\omega t)$

   travels in the $+x$ direction, while

   $\sin(kx+\omega t)$

   travels in the $-x$ direction.

   Hence this electromagnetic wave propagates along:

   $-\hat i$

3. Use the direction relation for electromagnetic waves

   In an electromagnetic wave,

   $\vec E \times \vec B$

   gives the direction of propagation.

   We already have:

   $\vec B \parallel \hat j$

   and propagation is along $-\hat i$.

   We need $\vec E$ such that

   $\vec E \times \hat j = -\hat i$

   Now,

   $\hat k \times \hat j = -\hat i$

   Therefore,

   $\vec E \parallel \hat k$

4. Use the magnitude relation

   For an electromagnetic wave in vacuum,

   $E = cB$

   Therefore,

   $E_0 = cB_0$

5. Match the phase

   Electric and magnetic fields in a plane electromagnetic wave are in phase, so $\vec E$ must also contain:

   $\sin(kx+\omega t)$

6. Write the electric field expression

   Thus,

   $\boxed{\vec E = B_0 c\,\sin(kx+\omega t)\,\hat k\;\text{V/m}}$

7. Check options

   • A: $B_0 c\sin(kx+\omega t)\hat k$ ✅ Correct
   • B: amplitude should be $cB_0$, not $B_0/c$ ❌
   • C: wrong sign/direction ❌
   • D: wrong phase form; would correspond to propagation in $+x$ ❌

Therefore, the correct option is:

$\boxed{A}$