The intensity of a laser beam is 2.5 x 1014 W/m2. The amplitude of the magnetic field in the beam is
(Given, εo =8.85 x 10−12 C2N−1m−2)
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → ~1.45 T
The intensity of an electromagnetic wave is its average energy density times c. With peak fields \( E_0 = cB_0 \),
\( \displaystyle I = \frac{1}{2}\varepsilon_0 E_0^{2}\,c = \frac{1}{2}\varepsilon_0 c^{3} B_0^{2} \)
\( \displaystyle B_0 = \sqrt{\frac{2I}{\varepsilon_0 c^{3}}} \)
\( \displaystyle B_0 = \sqrt{\frac{2 \times 2.5\times10^{14}}{8.85\times10^{-12} \times (3\times10^{8})^{3}}}\,\mathrm{T} \)
\( \displaystyle B_0 = \sqrt{\frac{5\times10^{14}}{2.39\times10^{14}}}\,\mathrm{T} = \sqrt{2.09}\,\mathrm{T} \approx 1.45\,\mathrm{T} \)