Shown below are pictorial and mathematical representations of an electromagnetic

Question

Shown below are pictorial and mathematical representations of an electromagnetic plane wave propagating through empty space. The electric field is parallel to the z-axis; the magnetic field is parallel to the y-axis. In which direction is the wave propagating? Explain how you can tell from the expressions for the electric field and magnetic field. Is the wave transverse or longitudinal? Explain in terms of the quantity or quantities that are oscillating.

Explanation / Answer

ITEM#1: To determine direction of propagation, consider a fixed point "x0" at time "t0" where EM wave haszero (0) magnitude and is increasing in value along the "x" axis. Thus, from the expression for electric (or magnetic) field, the value of {Sin(k*x0 + *t0) =0}. Now let time increase SMALL amount to new time "t1". Again using expression for electric (or magnetic) field, we see that {Sin(k*x0 + *t1)> Sin(k*x0 + *t0) = 0}. Referring to the diagram, the new value (at time "t1")of electric field magnitude thus arrives from the RIGHT(i.e., from "+x" direction). Hence, wave must propagatefrom Right to Left (i.e., into the "-x" direction). {Direction Of Propagation} = { "-x" Direction } {Wave is TRANSVERSE since oscillating electricand magnetic fields are PERPENDICULAR to propagation direction.} .

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