The key content of Maxwell electromagnetic field theory is two curl equations. In the free space, timing magnetic field produces timing electric field, the timing electric field then produces the timing magnetic field, and then the energy stream density of wave E×H makes vibration transmission in ether medium. Maxwell is the first physicist to predict the electric wave. In the past hundreds years, people have been waving the Maxwell curl theory instead of the true curl field theory in electric wave application in free space.

Radiation field’s inconformity with curl theory. Supposed that radiation field is conformed with curl theory, the civil 50Hz (or60Hz) supplier will generate up to 10×10⁷ V/m radiation field according to the Maxwell curl field on the condition of 1×1A×m, hence the radiation field is unlivable; when w is nearly equal to zero Hz, E=oo is beyond practice. Actually is reasonable when w is nearly equal to zero Hz according to Maxwell theory based on the direct current Ampere’s circuital law revision and electromagnetic induction, so the radiation equation derived from curl theory is beyond actual practice; the energy stream density of wave E×H is polynomial function of distance r, the electromagnetic energy outflow from sphere face S1 is not equal to the electromagnetic energy outflow from sphere face S1, the minus outflow from sphere face S1 indicates that the energy is from long distance place, which is unconfirmed with the actual practice. The field energy by curl theory and the wave energy are not inverse square rate of distance. Who really used the curl field in free space? The answer is no one.

Receiving field’s inconformity with curl theory. The key content of curl theory is mixed electro-magnetic field transmits energy stream density of wave E×H in the free space. Receiving is dipole antenna’s receiving E×H dependent vector field to form signal current under Lorentz action, not the energy stream’s (E×H) inflowing into antenna. E×H is polynomial function of distance r and also a minus energy, then E×H is not a inflowing energy, and the dipole antenna can’t receive the Eq in curl theory, because Eq may make the signal intensity not to be a polynomial function of distance r. Overall, the received electric wave is the wave in dependent radiation but the wave in curl theory (which is detailed interpreted in Chapter 4).

Transmission field’s inconformity with curl theory. Transmission field in dielectric waveguide (such as optical fiber communications and diver communications) are all independent vector Snell theory and Fresnel theory but energy stream of wave E×H in curl theory. In the transmission field of curl theory in metallic waveguide, the wave energy is conflict with energy conversation law, the minus transmission energy or distant oscillation energy source is beyond actual practice. Micro-wave engineers are utilizing another practical experience which was introduced in paragraph 1.6 and paragraph 5.2.

Wave beam form’s inconformity with curl theory. Radar big aperture antenna can gather beam in geometrical optical principle, the current on face is in accordance with General Lorentz magnetic force but not the energy stream of wave E×H theory. Slot antenna and phased array beam are formed by K₀/r² independent vector field superposition; the receiving signal density is inverse square law of distance, and not the K₀/r² field superposition in curl theory and even not the E×H energy superposition. Since more than 100 years of practical application, micro-wave experts have summarized some methods including geometrical optical method in independent vector field, Snell theory, Huygens principle, Fresnel principle, Lorentz magnetic force and Chebyshev polynomials. So it is sure to say that the curl theory has not been really utilized.

Timing magnetic field in betatron generator vacuum ring can’t generate accelerating electric field in curl theory, the linear I_Ddl at origin point can’t be conformed with the curl×H(p)=J_D at point P in free space.

The conclusion in this chapter is that the electric wave radiation, transmission, receiving and wave beam forming are unconfirmed with curl field theory.