Magnetic field in a plane electromagnetic wave is given by, $$\vec{B} = B_0 \sin(kx + \omega t)\hat{j}$$ T. Expression for corresponding electric field will be: (Where $$c$$ is speed of light)

We have been told that the magnetic field associated with a plane electromagnetic wave is

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

For any plane electromagnetic (e.m.) wave moving in free space the following facts are always true:

1. The electric field $$\vec E$$, the magnetic field $$\vec B$$ and the direction of wave propagation $$\hat n$$ are all mutually perpendicular, and they satisfy $$\hat n = \hat E \times \hat B\;.$$

2. The amplitudes are related by the universal relation

$$E_0 = c\,B_0\;,$$

where $$c$$ is the speed of light in vacuum.

3. The space-time variation (the “argument of the sine or cosine”) is exactly the same for $$\vec E$$ and $$\vec B$$, so they are in phase.

Let us now identify the propagation direction first. The magnetic field is along $$+\hat j$$ and the argument of the sine is $$kx + \omega t$$. For a harmonic term $$\sin(kx - \omega t)$$ the wave would move towards $$+\hat x$$, while $$\sin(kx + \omega t)$$ represents a wave travelling towards $$-\hat x$$. Hence the present wave moves along the negative $$x$$-axis, so

$$\hat n = -\hat i\;.$$

Next we determine the direction of $$\vec E$$. We need a unit vector $$\hat E$$ such that

$$\hat E \times \hat B = \hat E \times \hat j = -\hat i\;.$$

Recalling the right-hand rule for cross products,

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

so $$\hat E$$ must be $$\hat k$$. Therefore the electric field is directed along the $$z$$-axis.

We already know the amplitude relation $$E_0 = cB_0$$, and because the two fields are in phase, the sine factor remains unchanged. Putting all this information together we write

$$\vec E = E_0 \sin(kx + \omega t)\,\hat k = (cB_0)\sin(kx + \omega t)\,\hat k\;.$$

Simplifying the notation, the required expression is

$$\vec E = B_0\,c \,\sin(kx + \omega t)\,\hat k \;{\rm V\,m^{-1}}.$$

Among the given options, this matches Option C exactly.

Hence, the correct answer is Option C.