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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

Calculate the work done by an 85.0-kg man who pushes a crate 4.00 m up along a ramp that makes an angle of 20.0º20.0º with the horizontal. (See [link] .) He exerts a force of 500 N on the crate parallel to the ramp and moves at a constant speed. Be certain to include the work he does on the crate an
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Force equals mass time acceleration. Weight is a force and it can replace force in the equation. The acceleration would be gravity, which is an acceleration. To change from weight to mass divide by gravity (9.8 m/s^2).
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Practice Key Terms 2

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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