Representations of electromagnetic waves Shown below are pictorial and mathemati

Question

Representations of electromagnetic waves Shown below are pictorial and mathematical representations of an electromagnetic plane wave propagating through empty space. The electric field is parallel to the '-axis; the magnetic field is parallel to the y-axis. (x, y, z, t) = Eo sin(kx + omega t) B (x, y, z, t) = Bo sin(kx + omega t) At the instant shown in the figure, is the magnetic flux through the loop 1 rightarrow 2 rightarrow 3 rightarrow 4 rightarrow 1 positive, negative, or zero? Explain how you can tell from the figure. A short time later, will the magnetic flux through the loop be larger; smaller, or the same? Explain how you can tell from the figure.

Explanation / Answer

ITEM#2: Applying the Right-Hand Rule, the normal area vector for the area enclosed by closed path {1 --> 2 --> 3 --> 4 -->1} is in the "+y" direction. Since all Magnetic Field vectorswithin this enclosed area are also in the "+y" direction, the Magnetic Flux through this area is positive: {MagneticFlux Thru Area Enclosed By (1-2-3-4-1)} = {POSITIVE} Wave is propagating in the "-x" direction. On thediagram, this means that Magnetic Field vectors to the RIGHT of the closed loop area will replace current values. Thus,diagram indicates that Magnetic Field magnitudes in the enclosed area will DECREASE a short time later. Hence, theMagnetic Flux through this area will also decrease: {Change In Magnetic FluxThru (1-2-3-4-1)}} = {SMALLER} .

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