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EM-waves transport energyThe Poynting vector

= (1/2) oE2Using again B=E/c, one obtains the following equivalent expressions:

lectromagneticnergy densityJoule/m 3)

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indicates vector-product

Poyntingvector

Jm 2 sec

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Average power per unit area : Intensity

Intensity

I = c Erms 2I= c E rms 2 Intensity

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Example: Consider a light source of 250 Watts, emitting electromagneticradiation isotropically. Assuming the source emit harmonic EM-waves,calculate the amplitude of the electric filed of the wave at 1.8 m from thesource

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Point of view 1: LIGHT IS A WAVE

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Point of view 2: LIGHT IS A RADIATION FIELD OFQUANTIZED ENERGY PACKETS

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Point of view 3: LIGHT IS BOTH A WAVE AND A PARTICLE

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If light behaves as a particle,does it have

linear momentum ?angular momentum?

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Y

X

E

B

+ q

+ mZ

FB

Z

So, the mass m will gain some linearmomentum along the z-axis

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= work W done ( by the electric field E onthe charge ) per unit time; i. e . d W /dt q

We are trying to argue that the incident EM-wave:

does some work on the charge (i.e. deposit someenergy W),

and, as a consequence,

the charge feels some force FThe example above suggests:

dt

dW

c

1F

In any circumstance where light is beingabsorbed by a charge, there is a force on

that charge

On the other hand F= dp/dt. Here p is the momentum thecharge should have gained, and which should have beendelivered by the EM-wave.

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dt

d

c

1F

dt

d W p

Or,

The linear momentum thatlight delivers is equal to the energy that is absorbed,divided by c

c W p

We already knew that light carries energy (described by thePoynting vector). Now we also understand that it carries alsolinear momentum. In the expression above, W is the energyput into the charge q, which should have come from the EM-field (i.e. from the light).

Therefore,

p is the linear momentum ofthe light

W is the energy of the lightc is the speed of light

c W p

Classical physic goes this far as far on the understanding of

light.

But now we have quantum mechanics that tell us that, inmany respects, light behaves as particles. We mentioned inthe above sections that the energy W of a light-particle is,

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W is the energy of the light-particleh Plancks constant f frequency of the light

hf W

This light-particle, according to the arguments given above,will carry a linear momentum equal to W/c; that is,

p= W /c = hf /c = h/

p linear momentum of the light-particleh Plancks constant wavelength of the light

h p

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