Magnetics 6 Question 7
7. The mean intensity of radiation on the surface of the sun is about $10^{8} W / m^{2}$. The rms value of the corresponding magnetic field is closest to
(Main 2019, 12 Jan II)
(a) $1 T$
(b) $10^{2} T$
(c) $10^{-4} T$
(d) $10^{-2} T$
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Solution:
- Mean radiation intensity is
$$ \begin{aligned} I & =\varepsilon _0 c E _{rms}^{2} \\ & =\varepsilon _0 c\left(c B _{rms}\right)^{2} \quad \because \frac{E _{rms}}{B _{rms}}=c \\ & =\varepsilon _0 c^{3} B _{rms}^{2} \\ \Rightarrow \quad B _{rms} & =\sqrt{\frac{I}{\varepsilon _0 c^{3}}} \end{aligned} $$
Substituting the given values, we get
$$ \begin{aligned} & =\sqrt{\frac{10^{8}}{8.85 \times 10^{-12} \times\left(3 \times 10^{8}\right)^{3}}} \\ & =\sqrt{\frac{10^{8}}{8.85 \times 27 \times 10^{12}}} \approx \sqrt{\left(10^{-8}\right)} \approx 10^{-4} T \end{aligned} $$
