Ncert Exercises & Solutions

Poynting vectors S is defined as a vector whose magnitude is equal to the wave intensity and whose direction is along the direction of wave propagation. Mathematically, it is given by $S = \frac{1}{μ_{0}} E \times B$ . Show the nature of S versus t graph.

Hint: The electromagnetic wave propagates perpendicular to each electric field and magnetic field.

Step 1: Find the equation of electric field and magnetic field.

Consider an electromagnetic wave. Let E be varying along the y-axis, B is along the z-axis, and propagation of wave be along the x-axis. Then ExB will tell the direction of propagation of energy flow in an electromagnetic wave, along the x-axis.

Let, \vec{E} = E_{0} \sin (ωt - kx) \hat{j}

\vec{B} = B_{0} \sin (ωt - kx) \hat{k}

Step 2 : Find the equation of \vec{S} .

\vec{S} = \frac{1}{μ_{0}} (\vec{E} \times \vec{B}) = \frac{1}{μ_{0}} E_{o} B_{0} \sin^{2} (ωt - kx) [\hat{j} \times \hat{k}]

= \frac{E_{0} B_{0}}{μ_{0}} \sin^{2} (ωt - kx) \hat{I}

Step 3: Draw the graph.

The variation of

|S|

with time t will be as given in the figure below.

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