In quantum interpretation of the electromagnetic waves in vacuum the photon has the energy E = hw/2n and the momentump hk/2n. So the ratio E of the energy to the momentum is = c, the speed of light in vacuum. Similar relation can be obtained in classical electrodynamics as follows. Consider the time-averaged energy density of the electromagnetic field ɛ = B² /2µ0 + €0E² /2 for a plane wave propagating in vacuum along the z-direction. Calculate the time-averaged energy flux (Poynting flux) for such a wave S = E × H and confirm that its ratio to the time-averaged energy density ratio is equal to the speed of light in vacuum, S/e = c.
In quantum interpretation of the electromagnetic waves in vacuum the photon has the energy E = hw/2n and the momentump hk/2n. So the ratio E of the energy to the momentum is = c, the speed of light in vacuum. Similar relation can be obtained in classical electrodynamics as follows. Consider the time-averaged energy density of the electromagnetic field ɛ = B² /2µ0 + €0E² /2 for a plane wave propagating in vacuum along the z-direction. Calculate the time-averaged energy flux (Poynting flux) for such a wave S = E × H and confirm that its ratio to the time-averaged energy density ratio is equal to the speed of light in vacuum, S/e = c.
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![In quantum interpretation of the electromagnetic waves in vacuum the photon
has the energy E = hw/2n and the momentump= hk/2n. So the ratio
E
of the energy to the momentum is
= c, the speed of light in
k
vacuum.
Similar relation can be obtained in classical electrodynamics as follows.
Consider the time-averaged energy density of the electromagnetic field
ɛ = B² /2µ0 + €0 E² /2 for a plane wave propagating in vacuum along the
z-direction. Calculate the time-averaged energy flux (Poynting flux) for such a
wave S = E × H and confirm that its ratio to the time-averaged energy
density ratio is equal to the speed of light in vacuum, S/e = c.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6128a30d-be3c-4f5f-a17a-54eaa3ca9284%2Fd60ec218-dcd7-4fa7-a52f-e50a034b8342%2Fwghzyf_processed.png&w=3840&q=75)
Transcribed Image Text:In quantum interpretation of the electromagnetic waves in vacuum the photon
has the energy E = hw/2n and the momentump= hk/2n. So the ratio
E
of the energy to the momentum is
= c, the speed of light in
k
vacuum.
Similar relation can be obtained in classical electrodynamics as follows.
Consider the time-averaged energy density of the electromagnetic field
ɛ = B² /2µ0 + €0 E² /2 for a plane wave propagating in vacuum along the
z-direction. Calculate the time-averaged energy flux (Poynting flux) for such a
wave S = E × H and confirm that its ratio to the time-averaged energy
density ratio is equal to the speed of light in vacuum, S/e = c.
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