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  4. Suppose that intensity of a laser is ((315/π)) W / m 2 . The rms electric field, in units of V / m associated with this source is close to the nearest integer is (ϵ0=8.86 × 10-12 C 2 Nm -2 ; c =3 × 108 ms -1)

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Q. Suppose that intensity of a laser is $\left(\frac{315}{\pi}\right) W / m ^{2} .$ The rms electric field, in units of $V / m$ associated with this source is close to the nearest integer is
$\left(\epsilon_{0}=8.86 \times 10^{-12} C ^{2} Nm ^{-2} ; c =3 \times 10^{8} ms ^{-1}\right)$

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Solution:

$I =\epsilon_{0} E _{ rms }^{2} C$
$E _{ rms }^{2}=\frac{ I }{\epsilon_{0} C }$
$=\frac{315}{\pi \epsilon_{0}} \times \frac{1}{ C }$
$=\frac{4 \times 315}{4 \pi \epsilon_{0}} \times \frac{1}{3 \times 10^{8}}$
$=\frac{4 \times 315 \times 9 \times 10^{9}}{3 \times 10^{8}}$
$E _{ rms }^{2}=4 \times 315 \times 30$
$E _{ rms }=2 \sqrt{315 \times 30}$
$=194.42$