Final answer:
The equation for the electric field in the phasor domain that corresponds to the given magnetic field is E = (3 × 10^8)(4)e^-jκx z [V/m], assuming that electromagnetic fields are perpendicular to each other and to the direction of wave propagation, with E/H = speed of light in vacuum.
Step-by-step explanation:
To find the equation for the electric field of an electromagnetic wave in the phasor domain associated with the given magnetic field H, we will use Maxwell's equations in free space, which relate the electric field E to the magnetic field B (note that in the phasor domain, B is replaced by H for magnetic field intensity). Given a magnetic field H = -4e-jkx y [A/m], and knowing that electromagnetic waves have their electric and magnetic fields perpendicular to each other and to the direction of propagation, we can start by assuming that the electric field will have a component in the z-direction since the magnetic field is in the y-direction.
Moreover, the relationship between the magnitudes of the electric and magnetic fields in free space (vacuum) is given by the speed of light, c, where E/H = c and c is approximately 3 × 108 m/s. Therefore, the electric field phasor can be written as E = c|H|z = (3 × 108)(4)e-jkx z [V/m]. Here, the positive sign indicates that the electric field is in phase with the magnetic field, and the choice of direction (z-axis) ensures perpendicularity to H.
Finally, the orientation of the electric field with respect to the coordinate axes also indicates that the wave is propagating along the x-axis, as electric and magnetic fields are always perpendicular to the direction of wave propagation.