Q153 / 160 · TS EAMCET 2022 (20 Jul Shift 1) · Physics

On a particular day, the sun delivers an average power of $\left(\frac{6}{\pi} \times 10^3\right) \frac{\mathrm{W}}{\mathrm{m}^2}$ to the top of Earth's atmosphere. Find the amplitude of magnetic field for the electromagnetic waves above atmosphere. (Take $\mu_0=4 \pi \times 10^{-7}$ SI unit)

  • A
    $5 \times 10^{-5} \mathrm{~T}$
  • Correct answer
    B
    $4 \times 10^{-6} \mathrm{~T}$
  • C
    $6 \times 10^{-6} \mathrm{~T}$
  • D
    $3 \times 10^{-5} \mathrm{~T}$

Solution

$\begin{aligned} & \mathrm{I}=\frac{\mathrm{B}_0^2 \mathrm{C}}{2 \mu_0} \\ & \Rightarrow \quad \mathrm{B}_0^2=\frac{2 \mu_0 \mathrm{I}}{\mathrm{C}} \\ & \Rightarrow \quad \mathrm{B}_0^2=\frac{2 \times 4 \pi \times 10^{-7} \times \frac{6}{\pi} \times 10^3}{3 \times 10^8} \\ & \Rightarrow \quad \mathrm{B}_0^2=16 \times 10^{-12} \\ & \Rightarrow \quad \mathrm{B}_0=4 \times 10^{-6} \mathrm{~T}\end{aligned}$

Hence, the correct answer is option: 'B'.

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