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  4. The intensity of the light from a bulb incident on a surface is 0.22 W / m 2. The amplitude of the magnetic field in this light-wave is × 10-9 T. (Given: Permittivity of vacuum ϵ0=8.85 × 10-12 C 2 N -1 m -2, speed of light in vacuum c =3 × 108 ms -1 )

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Q. The intensity of the light from a bulb incident on a surface is $0.22 \,W / m ^{2}$. The amplitude of the magnetic field in this light-wave is ______ $\times 10^{-9} T$.
(Given : Permittivity of vacuum $\epsilon_{0}=8.85 \times 10^{-12} C ^{2} N ^{-1} m ^{-2}$, speed of light in vacuum $c =3 \times 10^{8} ms ^{-1}$ )

JEE MainJEE Main 2022Electromagnetic Waves

Solution:

$I =\left(\frac{1}{2} \varepsilon_{0} E _{0}^{2}\right) C$
$\Rightarrow E _{0} \Rightarrow \sqrt{\frac{2 I }{\varepsilon_{0} C }}$
$ \Rightarrow \sqrt{\frac{2 \times 0.22}{8.85 \times 10^{-12} \times 3 \times 10^{8}}}=12.873$
$B \Rightarrow \frac{ E _{0}}{ C } \Rightarrow \frac{12.873}{3 \times 10^{8}}$
$=4.291 \times 10^{-8}=43 \times 10^{-9}$