First slide

Intensity of electromagnetic wave

Question

The intensity of TV broad cast station of E = 800 Sin (10⁹ t - k x) V/m is ......... and the wave length in meter is ..............

Moderate

A

850 Wm^-2 ; 0.6 $π$
B

425 Wm^-2 ; 0.6 $π$
C

850 Wm^-2 ; 0.3 $π$
D

425 Wm^-2 ; 0.3 $π$

Solution

$\begin{array}{rcl} E & = & 800 \sin (10^{9} t - kx) {Vm}^{- 1} \\ I & = & u_{avg} x C \\ = & \frac{1}{2} ε_{0} {E_{0}}^{2} x C \\ = & \frac{1}{2} x 8.85 x 10^{- 12} x {(800)}^{2} x 3 x 10^{8} \\ = & 849.6 \\ \approx & 850 {Wm}^{- 2} \\ ω & = & 10^{9}, 2 πn = 10^{9}, n = \frac{10^{9}}{2 π}; C = nλ \\ λ & = & \frac{C}{n} = \frac{3 x 10^{8}}{10^{9}} x 2 π; \\ λ & = & 0.6 π m \end{array}$

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