The electric field of an electromagnetic wave in free space is represented as $$\vec{E} = E_0 \cos(\omega t - kz)\hat{i}$$. The corresponding magnetic induction vector will be :

For an electromagnetic wave, the relationship between the electric field and the magnetic field is governed by the following principles:

1. The magnitudes are related by: $$B_0 = \frac{E_0}{c}$$, where $$c$$ is the speed of light.

2. The direction of propagation is along $$\vec{E} \times \vec{B}$$.

3. Both fields have the same phase and propagation direction.

Given: $$\vec{E} = E_0 \cos(\omega t - kz)\hat{i}$$

The wave propagates in the $$+z$$ direction (from the $$-kz$$ term).

Since $$\hat{i} \times \hat{j} = \hat{k}$$ (the direction of propagation), the magnetic field must be along $$\hat{j}$$.

The magnitude of the magnetic field amplitude is $$\frac{E_0}{c}$$, and it has the same phase $$(\omega t - kz)$$.

Therefore:

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

The correct answer is $$\vec{B} = \frac{E_0}{C} \cos(\omega t - kz)\hat{j}$$.