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.4) State the poynting vector equation.5) Comment on attenuation constant.

To find the intrinsic impedance of the medium, we can use the formula Z = sqrt(mu/epsilon), where mu is the permeability of free space and epsilon is the permittivity of the medium. In this case, since we are in free space, mu = mu0 (permeability of free space) and epsilon = epsilon0 (permittivity of free space). Therefore, the intrinsic impedance 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 E is given as E(z,t) = 50 cos(wt - gz) a, where a represents the direction of the electric field. So, the direction of the electromagnetic wave is in the direction of the vector a.

To find the magnetic field vector, we can use the relationship between the electric field and magnetic field in an electromagnetic wave. 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. In this case, the magnetic field vector B = (1/c) * 50 cos(wt - gz) a.

The Poynting vector equation relates the electric field, magnetic field, and the direction of propagation of the electromagnetic wave. The Poynting vector S is given by the equation S = (1/mu) * E x B, where x represents the cross product. In this case, the Poynting vector equation is S = (1/mu0) * (50 cos(wt - gz) a) x ((1/c) * 50 cos(wt - gz) a).

The attenuation constant represents the rate at which the amplitude of the electromagnetic wave decreases as it propagates through a medium. In this case, since we are in free space, there is no medium to cause attenuation. Therefore, the attenuation constant is zero.