Question8) [swHW part(b), seHW part(a)] Consider two linearly-polarized plane wave pulses of light with the same duration, the same wavelength, the same polarization, and the same maximum amplitude, and propagating in vacuum in exactly-opposite directions. The pair will form a standing electric field wave in places where they overlap. As we know, such a standing wave momentarily has zero electric field amplitude everywhere at one infinitesimal instant in time, and thus the two combined waves must, at some single instant in time, have zero electric field everywhere in space.
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a) At the one instant in time when the two pulses result in zero electric field everywhere in space, describe the magnetic field everywhere in space.
b) Propose an explanation of how the energy of a standing light wave is stored when the electric field is zero everywhere in space. For your answer please propose a testable hypothesis that is consistent with all the laws of physics that you know. Be sure your hypothesis could potentially be disproven (this is called a "falsifiable" hypothesis, and is considered a stronger type of scientific hypothesis).
Studdy Solution
STEP 1
1. Two linearly-polarized plane wave pulses are propagating in opposite directions.
2. They have the same duration, wavelength, polarization, and maximum amplitude.
3. The waves form a standing electric field wave in regions where they overlap.
4. At a certain instant, the electric field is zero everywhere in space.
STEP 2
1. Describe the magnetic field at the instant when the electric field is zero.
2. Propose a hypothesis for energy storage when the electric field is zero.
STEP 3
At the instant when the electric field is zero everywhere, the magnetic field is at its maximum amplitude everywhere in space.
This is because, in electromagnetic waves, the electric and magnetic fields are perpendicular to each other and oscillate in phase. When one field is at a minimum, the other is at a maximum.
STEP 4
The energy of the standing wave is stored in the magnetic field when the electric field is zero.
This is consistent with the principle of conservation of energy, where the energy oscillates between the electric and magnetic fields.
STEP 5
Propose a testable hypothesis: "At the instant when the electric field is zero everywhere, the energy of the standing wave is entirely stored in the magnetic field, which reaches its maximum amplitude."
This hypothesis can be tested by measuring the magnetic field at the instant when the electric field is zero and verifying that it corresponds to the energy expected from the initial conditions of the wave pulses.
The magnetic field is at its maximum amplitude when the electric field is zero, and the energy is stored in the magnetic field.
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