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  • Explain how the energy and amplitude of an electromagnetic wave are related.
  • Given its power output and the heating area, calculate the intensity of a microwave oven’s electromagnetic field, as well as its peak electric and magnetic field strengths

Anyone who has used a microwave oven knows there is energy in electromagnetic waves    . Sometimes this energy is obvious, such as in the warmth of the summer sun. Other times it is subtle, such as the unfelt energy of gamma rays, which can destroy living cells.

Electromagnetic waves can bring energy into a system by virtue of their electric and magnetic fields . These fields can exert forces and move charges in the system and, thus, do work on them. If the frequency of the electromagnetic wave is the same as the natural frequencies of the system (such as microwaves at the resonant frequency of water molecules), the transfer of energy is much more efficient.

Connections: waves and particles

The behavior of electromagnetic radiation clearly exhibits wave characteristics. But we shall find in later modules that at high frequencies, electromagnetic radiation also exhibits particle characteristics. These particle characteristics will be used to explain more of the properties of the electromagnetic spectrum and to introduce the formal study of modern physics.

Another startling discovery of modern physics is that particles, such as electrons and protons, exhibit wave characteristics. This simultaneous sharing of wave and particle properties for all submicroscopic entities is one of the great symmetries in nature.

The propagation of two electromagnetic waves is shown in three dimensional planes. The first wave shows with the variation of two components E and B. E is a sine wave in one plane with small arrows showing the vibrations of particles in the plane. B is a sine wave in a plane perpendicular to the E wave. The B wave has arrows to show the vibrations of particles in the plane. The waves are shown intersecting each other at the junction of the planes because E and B are perpendicular to each other. The direction of propagation of wave is shown perpendicular to E and B waves. The energy carried is given as E sub u. The second wave shows with the variation of the components two E and two B, that is, E and B waves with double the amplitude of the first case. Two E is a sine wave in one plane with small arrows showing the vibrations of particles in the plane. Two B is a sine wave in a plane perpendicular to the two E wave. The two B wave has arrows to show the vibrations of particles in the plane. The waves are shown intersecting each other at the junction of the planes because two E and two B waves are perpendicular to each other. The direction of propagation of wave is shown perpendicular to two E and two B waves. The energy carried is given as four E sub u.
Energy carried by a wave is proportional to its amplitude squared. With electromagnetic waves, larger E size 12{E} {} -fields and B size 12{B} {} -fields exert larger forces and can do more work.

But there is energy in an electromagnetic wave, whether it is absorbed or not. Once created, the fields carry energy away from a source. If absorbed, the field strengths are diminished and anything left travels on. Clearly, the larger the strength of the electric and magnetic fields, the more work they can do and the greater the energy the electromagnetic wave carries.

A wave’s energy is proportional to its amplitude    squared ( E 2 size 12{E rSup { size 8{2} } } {} or B 2 size 12{B rSup { size 8{2} } } {} ). This is true for waves on guitar strings, for water waves, and for sound waves, where amplitude is proportional to pressure. In electromagnetic waves, the amplitude is the maximum field strength    of the electric and magnetic fields. (See [link] .)

Thus the energy carried and the intensity     I size 12{I} {} of an electromagnetic wave is proportional to E 2 size 12{E rSup { size 8{2} } } {} and B 2 size 12{B rSup { size 8{2} } } {} . In fact, for a continuous sinusoidal electromagnetic wave, the average intensity I ave size 12{I rSub { size 8{"ave"} } } {} is given by

I ave = 0 E 0 2 2 , size 12{I rSub { size 8{"ave"} } = { {ce rSub { size 8{0} } E rSub { size 8{0} } rSup { size 8{2} } } over {2} } } {}

where c size 12{c} {} is the speed of light, ε 0 size 12{ε rSub { size 8{0} } } {} is the permittivity of free space, and E 0 size 12{E rSub { size 8{0} } } {} is the maximum electric field strength; intensity, as always, is power per unit area (here in W/m 2 size 12{"W/m" rSup { size 8{2} } } {} ).

The average intensity of an electromagnetic wave I ave size 12{I rSub { size 8{"ave"} } } {} can also be expressed in terms of the magnetic field strength by using the relationship B = E / c size 12{B= {E} slash {c} } {} , and the fact that ε 0 = 1 / μ 0 c 2 size 12{ε rSub { size 8{0} } = {1} slash {μ rSub { size 8{0} } } c rSup { size 8{2} } } {} , where μ 0 size 12{μ rSub { size 8{0} } } {} is the permeability of free space. Algebraic manipulation produces the relationship

Questions & Answers

Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
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what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
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abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
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I'm interested in nanotube
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Ramkumar Reply
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Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Basic physics for medical imaging. OpenStax CNX. Feb 17, 2014 Download for free at http://legacy.cnx.org/content/col11630/1.1
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