The intensity of TV broad cast station of E = 800Sin(10⁹t - kx)V/M is __ and the wave length in meter is _

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850 wm^-2 ; 0.3π

425 wm^-2 ; 0.3π

850 wm^-2 ; 0.6π

425 wm^-2 ; 0.6π

answer is A.

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Detailed Solution

$I = \frac{1}{2} ϵ_{0} E^{2} C$

$\begin{array}{r} = \frac{1}{2} \times 8.85 \times 10^{- 12} \times (800)^{2} \times 3 \times 10^{8} \end{array}$

$\begin{array}{r} = 849.6 \\ \approx 850 {Wm}^{- 2} \end{array}$

$\begin{aligned} ω = 10^{9}, 2 π n = 10^{9}, n = \frac{10^{9}}{2 π}; C = n λ \\ λ = \frac{C}{n} = \frac{3 \times 10^{8}}{10^{9}} \times 2 π; \\ λ = 0.6 π m \end{aligned}$

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