# Being of Electromagnetic (EM) radiation pressure

Dr. S. S. VERMA; Department of Physics, S.L.I.E.T., Longowal; Distt.-Sangrur (Punjab)-148 106

2022-01-04 18:02:32

Credit: Dr. S. S. VERMA

Wave-particle duality still remaining a mystery, we can say that we are always surrounded by energy in the forms of waves (mechanical or electromagnetic) and particles.  We always feel air blowing, see water flowing and light shining on us. When these all interact with a body, they always transfer energy or say momentum to the body and that is why we see things bending, blowing, flying when high speed winds and strong water waves or particles interact with the objects. The vibration of an electric charge generates the electromagnetic waves which are composed of both an electric and a magnetic field components perpendicular to each other as well as perpendicular to the direction wave propagation. In case of light (which also EM wave/radiation) particularly, the particle concept is taken over by wave when the base particle “photon” is said to have rest mass “zero”.

Energy and momentum in EM waves

The overall EM waves spectrum and for EM radiation in the visible range i.e. light is shown in Table 1a & b (Ref.1).  When an electromagnetic wave of any frequency (c=fλ) is scattered or absorbed by an object, the wave exerts a radiation pressure on the object [1,2]. The electromagnetic radiation pressure is the type of mechanical pressure exerted upon on the surface of any object due to the exchange of momentum between the object and the electromagnetic field.  The associated force due to radiation pressure is called the radiation pressure force, or sometimes just the force of light. In electrostatics and magnetostatics the Newton’s third law holds good, but not in electrodynamics and the proof of conservation of momentum rests on the cancellation of internal forces, which follows from the Newton’s third law. Tempering with the third law will always place conservation of momentum in jeopardy, and there is no principle in Physics more sacred than conservation of momentum. Therefore, momentum conservation is rescued in electrodynamics by the realization that the fields themselves carry momentum same as they carry energy with them. The momentum conservation in EM radiation is restored only by adding the EM radiation momentum to the mechanical momentum of the charges.

Table 1a (Ref. 1)

Table 1b (Ref. 1)

The energy per unit volume stored in EM fields is given as:

u=12?0E2+1μ0B2                                                 (1)

In case of a monochromatic (having single frequency or wavelength) plane wave

B2=1c2E2=μ0?0E2                                                  (2)

As the wave ravels, it carries energy or energy density of EM radiation/waves which is proportional to the square of the amplitude of the electric (or magnetic) field component and is given as u= ?0E2. The energy flux density (energy per unit area, per unit time) transported by the fields is given by the Poynting’s vector S=1μ0(EXB). EM fields not only carry energy, they also carry momentum and the momentum density stored in the fields is ℘=1c2S . The time average values of these quantities can be written as:  <u>= 12?0E2;    <S>=12c?0E02 ;     <℘>=12c?0E02

The average power per unit area transported by an EM wave is called the intensity:

I  ≡  <S>  =   12c?0E02                                                  (3)

As in the case of conservation of charge and conservation of energy, conservation of momentum can be given a differential formulation as ∂tmech+em=?T, where T is momentum flux density or electromagnetic stress (force per unit area) acting on the surface. Thus, when light falls on a perfect absorber it delivers its momentum to the surface.  In a time ?t the momentum transfer is  ?p=<℘>Ac?t. So the radiation is force/area, and force is change in momentum w.r.t. time. Hence EM radiation should exert a pressure on objects when it hits them.  Radiation pressure= F/A = (dp/dt)/A = [d(energy/speed)/dt]/A = [power/speed]/A = [power/area]/speed = I/c, where, I = power/area is called wave’s irradiance. If the radiation reflects, then the momentum is twice and so the radiation is also twice.

Concern about and understanding of EM radiation pressure in general and light as in particular have made it possible to use it in many exotic scientific and technological applications. Most natural light sources exert negligibly small forces on objects and this subtle effect was first demonstrated by the American physicists Ernest Fox Nichols and Gordon Hull in 1903. However, this radiation pressure can be more consequential in with high powered lasers or a number of astronomical settings. Worldly applications of EM radiation pressure became feasible with the arrival of lasers in the 1960s. Because of the small diameters of output laser beams  and their excellent focusing properties, laser intensities are generally orders of magnitude larger than the intensities of natural light sources. On the largest scale, the most powerful laser systems are being employed to compress and heat target materials in nuclear fusion inertial confinement schemes. Further, the light radiation forces from table-top laser systems are also being used to manipulate atoms and microscopic objects. The techniques of laser cooling and trapping, pioneered by the Physics Nobelists (1997) Steven Chu, William Phillips, and Claude Cohen-Tannoudji, slow a gas of atoms in an “optical molasses” of intersecting laser beams. Using the laser cooling techniques, temperatures below 10−6 K (one-millionth of a degree above absolute zero) have been achieved. In a recently developed “Optical tweezers” is a related technique in which a tightly focused laser beam exerts a radiation force large enough to deflect, guide, and trap micron-sized objects ranging from dielectric spheres to biological samples such as viruses, single living cells, and organelles within cells. Development of optical tweezers have been awarded Physics Nobel Prize in 2018 to Arthur Ashkin.

Table 2

 Sl No. Mode of EM radiations Frequency range Light 405–790 THz Radio & TV 3kHz-300GHz Phone/Mobile generation 1G 150-900MHz 2G 900MHz-1.8GHz 3G 1.6-2.0GHz 4G 2.0-8.0GHz 5G 3.0-300GHz 6G >95GHz (750-1100GHz)

Table 3 (Ref. 4)

References

1. Introduction to Electrodynamics by David J Griffiths, Prentice-Hall of India Private Limited, New Delhi (1999), Chapter-9: 9.2.3-Energy and momentum of Electromagnetic waves, pp.380.
2. Classical Electrodynamics (3rd Edition) by J.D. Jackson, John Wiley & Sons Inc. (USA) (1999), Chapter-6:6.6-Poynting’s theorem and conservation of energy and momentum for a system of charged particles and electromagnetic fields, pp.258.
3. S. Wall et al, Real-world cell phone radiofrequency electromagnetic field exposures, Environmental Research 171 (2019) 581–592.
4. C. Törnevik et al., Time Averaged Power Control of a 4G or a 5G Radio Base Station for RF EMF Compliance, in IEEE Access, vol. 8, pp. 211937-211950, 2020, doi: 10.1109/ACCESS.2020.3039365.