Electromagnetic Waves in a Vacuum
Problem 1
Two parallel strips of metal of negligible resistance have width
Choose some instant of time,
- Plot the magnitude of the electric field,
, and magnetic field, (between the strips) as a function of the longitudinal position along the strips. - What are the directions of the vectors
and ? - Compute the power supplied by the voltage source.
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You can do this problem either by transmission line analysis (inductance, capacitance per unit length, etc.) or by physical reasoning on how electromagnetic fields propagate between the plates (free space).
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-
, plots shown below.
points from upper to lower strip, is parallel to the strips (pointing into the paper).- Power supplied by voltage source =
Problem 2
Sunlight with B-field
- Find
, the direction, the wavelength and the frequency of the incident sunshine; - Find the E-field of the incident sunshine;
- Find the Poynting vector of the incident sunshine;
- Find the reflected E-field;
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What are the boundary conditions at the surface of a perfect conductor?
- Find the total E-field;
- Due to global warming, this piece of ice has just melted, exposing the totally absorbing black rocks underneath. How much additional energy per second is the Earth absorbing due to this melted ice? How does it compare with the average electrical power consumption of the world (about four times the US power consumption, which is the average power consumption per person times the US population)?
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- The direction
; the wavelength is nm; the frequency of the incident sunshine Hz; and , thus webers/m . - The incident E-field =
Newtons/Coulomb - The Poynting vector of the incident light:
- The reflected E-field =
Newtons/Coulomb - The total E-field =
Newtons/Coulomb, i.e. a propagating wave in the direction and a standing wave in the direction; - The additional energy per second absorbed by the Earth is
which is much bigger than the Watts of the average electrical power consumption of the world ( billion people world-wide times 100 Watts/person, or see e.g. Orders of magnitude (power)), so global warming will accelerate faster and faster, as more and more ice melts.