14.2 Problems
645
14.60 At the orbit of the earth, the power of sunlight is 1,300 Wm −2 . Estimate the
amplitude of the electric field if we assume that all the power arrives on the
earth in a monochromatic wave.
[University of Aberystwyth, Wales 2004]
14.61 A typical value for the amplitude of the E-field for sunlight at the surface of
Mars is 300 V/m Calculate the amplitude of the corresponding B-field and
estimate the flux of radiation at the surface of Mars.
[University of Manchester 2006]
14.62 Show that
|E|
|H | = 377
[University of Aberystwyth, Wales]
14.63 Calculate the skin depth in copper (conductivity 6×10 7 −1 /m) of radiation
of frequency 20 kilocycles/s. Take μ, the relative permeability of copper, as
unity.
[University of Newcastle upon Tyne 1964]
14.64 Copper has an electrical conductivity σ = 5.6 × 10 7 −1 /m and a magnetic
permeability μ = 1. On this basis estimate the order of magnitude of the
depth to which radiation at a frequency of 3000 Mc/s can penetrate a large
copper screen.
[University of Bristol 1959]
14.65 Show that the skin depth in a good conductor is
1
2 ωσ μμ 0
−1/2
where the
symbols have their usual meaning.
[University of Newcastle upon Tyne 1964]
14.66 If the maximum electric field in a light wave is 10 −3 V/m, find how much
energy is transported by a beam of 1 cm 2 cross-sectional area.
[University of Durham 1962]
14.67 Prove Poynting’s theorem, namely
div (E × H) + E.
∂D
∂t
+ H.
∂E
∂t
+ E. j = 0
What is the interpretation of this equation?
[University of Durham 1962][University of New Castle upon Tyne 1965]
14.68 From Maxwell’s equations, one can derive a wave equation for a dielectric
of the form
∇
2 E − μ 0 ε 0 ε r
∂ 2 E
∂t 2 − μ 0 σ N
∂ E
∂t
= 0
where E is the electric field, t is the time, ε r is the relative permittivity and
σ N is the electrical conductivity. Hence by substituting a travelling wave
solution into the wave equation derive a dispersion relation of the form
645
14.60 At the orbit of the earth, the power of sunlight is 1,300 Wm −2 . Estimate the
amplitude of the electric field if we assume that all the power arrives on the
earth in a monochromatic wave.
[University of Aberystwyth, Wales 2004]
14.61 A typical value for the amplitude of the E-field for sunlight at the surface of
Mars is 300 V/m Calculate the amplitude of the corresponding B-field and
estimate the flux of radiation at the surface of Mars.
[University of Manchester 2006]
14.62 Show that
|E|
|H | = 377
[University of Aberystwyth, Wales]
14.63 Calculate the skin depth in copper (conductivity 6×10 7 −1 /m) of radiation
of frequency 20 kilocycles/s. Take μ, the relative permeability of copper, as
unity.
[University of Newcastle upon Tyne 1964]
14.64 Copper has an electrical conductivity σ = 5.6 × 10 7 −1 /m and a magnetic
permeability μ = 1. On this basis estimate the order of magnitude of the
depth to which radiation at a frequency of 3000 Mc/s can penetrate a large
copper screen.
[University of Bristol 1959]
14.65 Show that the skin depth in a good conductor is
1
2 ωσ μμ 0
−1/2
where the
symbols have their usual meaning.
[University of Newcastle upon Tyne 1964]
14.66 If the maximum electric field in a light wave is 10 −3 V/m, find how much
energy is transported by a beam of 1 cm 2 cross-sectional area.
[University of Durham 1962]
14.67 Prove Poynting’s theorem, namely
div (E × H) + E.
∂D
∂t
+ H.
∂E
∂t
+ E. j = 0
What is the interpretation of this equation?
[University of Durham 1962][University of New Castle upon Tyne 1965]
14.68 From Maxwell’s equations, one can derive a wave equation for a dielectric
of the form
∇
2 E − μ 0 ε 0 ε r
∂ 2 E
∂t 2 − μ 0 σ N
∂ E
∂t
= 0
where E is the electric field, t is the time, ε r is the relative permittivity and
σ N is the electrical conductivity. Hence by substituting a travelling wave
solution into the wave equation derive a dispersion relation of the form