Final answer:
In physics, especially when examining electromagnetic waves, central attributes include amplitude, frequency, wavelength, travel direction, and associated magnetic fields.
Step-by-step explanation:
When analyzing an electromagnetic wave, such as the given electric field E=(ax³+ay²)e⁻ˆᵋkz, several characteristics are important: the amplitude, frequency, wavelength, direction of travel, and associated magnetic field. In this case, the electric field components suggest that the wave may not be linearly polarized, as both x and y components vary differently. Additional information would be necessary to fully determine the wave's polarization.
For a plane electromagnetic wave traveling along the positive y-axis, with an electric field along the z-axis, we can describe the wave function of the electric field as E(z, t) = 10 V/m cos(kz - ωt), where ω is the angular frequency that can be related to the given frequency f by ω = 2πf. The magnetic field, by Maxwell's equations, can be described as being perpendicular to both the direction of propagation and the electric field, suggesting a wave function B(x, t) = (B0/μ0) cos(kz - ωt).
For the displacement current through a tube, the expression would involve integrating the time-derivative of the electric field over the cross-sectional area of the tube. According to Maxwell's equations, the displacement current density is ε0 dE/dt, where ε0 is the permittivity of free space.