Q154 / 160 · TS EAMCET 2019 (04 May Shift 2) · Physics
In a travelling plane electromagnetic wave, the maximum magnetic field is $1.26 \times 10^{-4} \mathrm{~T}$. The intensity of the wave is (Assume, $\mu_0=1.26 \times 10^{-6} \mathrm{H} / \mathrm{m}$ )
- A$1.56 \times 10^6 \frac{\mathrm{W}}{\mathrm{m}^2}$
- Correct answerB$1.89 \times 10^6 \frac{\mathrm{W}}{\mathrm{m}^2}$
- C$8.92 \times 10^5 \frac{\mathrm{W}}{\mathrm{m}^2}$
- D$4.62 \times 10^6 \frac{\mathrm{W}}{\mathrm{m}^2}$
Solution
Given, maximum magnetic field,
$\begin{aligned}<br />& B_0=1.26 \times 10^{-4} \mathrm{~T} \\<br />& \mu_0=1.26 \times 10^{-6} \mathrm{H} / \mathrm{m}<br />\end{aligned}$
$\therefore$ Intensity of EMW (Electromagentic wave) is given by
$\begin{aligned}<br />I & =\frac{1}{2} \frac{B_0^2 c}{\mu_0}=\frac{1}{2} \times \frac{\left(1.26 \times 10^{-4}\right)^2 \times 3 \times 10^8}{1.26 \times 10^{-6}} \\<br />& =\frac{1}{2} \times \frac{1.26 \times 1.26 \times 10^{-8} \times 3 \times 10^8}{1.26 \times 10^{-6}} \\<br />& =0.63 \times 3 \times 10^6=1.89 \times 10^6 \mathrm{~W} / \mathrm{m}^2<br />\end{aligned}$
$\begin{aligned}<br />& B_0=1.26 \times 10^{-4} \mathrm{~T} \\<br />& \mu_0=1.26 \times 10^{-6} \mathrm{H} / \mathrm{m}<br />\end{aligned}$
$\therefore$ Intensity of EMW (Electromagentic wave) is given by
$\begin{aligned}<br />I & =\frac{1}{2} \frac{B_0^2 c}{\mu_0}=\frac{1}{2} \times \frac{\left(1.26 \times 10^{-4}\right)^2 \times 3 \times 10^8}{1.26 \times 10^{-6}} \\<br />& =\frac{1}{2} \times \frac{1.26 \times 1.26 \times 10^{-8} \times 3 \times 10^8}{1.26 \times 10^{-6}} \\<br />& =0.63 \times 3 \times 10^6=1.89 \times 10^6 \mathrm{~W} / \mathrm{m}^2<br />\end{aligned}$
Hence, the correct answer is option: 'B'.