In free space E (z,t) = 50 cos(wt -gz) a, (V/m). Find the following.1) Intrinsic impedance of the medium.2) State the direction of the electromagnetic3) Find a magnetic field vector

To find the intrinsic impedance of the medium, we can use the formula Z = sqrt(mu/epsilon), where mu is the permeability of the medium and epsilon is the permittivity of the medium. In free space, mu = mu0 (permeability of free space) and epsilon = epsilon0 (permittivity of free space). Therefore, the intrinsic impedance of the medium is Z = sqrt(mu0/epsilon0).

The direction of the electromagnetic wave can be determined by looking at the direction of the electric field vector. In this case, the electric field vector is given as E(z,t) = 50 cos(wt - gz) a, where a is the unit vector in the direction of propagation. Since the cosine function oscillates between positive and negative values, the electric field vector oscillates in the direction of a, which is the direction of propagation of the wave.

To find the magnetic field vector, we can use the relationship between the electric field and magnetic field in an electromagnetic wave. In free space, the magnetic field vector B is related to the electric field vector E by the equation B = (1/c) * E, where c is the speed of light in vacuum. Therefore, the magnetic field vector is B(z,t) = (1/c) * 50 cos(wt - gz) a, where a is the unit vector in the direction of propagation.