Question

A laser beam has intensity 2.5 × 10¹⁴ W m⁻². Find amplitudes of electric and magnetic fields in the beam.

Answer 1

Given:
Intensity, I = 2.5 × 10¹⁴ W/m²
We know:
$I=\frac{1}{2}{\in }_0{E_0}^{2}c$
$$\begin{gathered} \Rightarrow {E_0}^2=\frac{2I}{{\mathit{\in }}_{0}c} \\ \Rightarrow E_0=\sqrt{\frac{2I}{{\mathit{\in }}_{0}c}} \\ \Rightarrow E_0=\sqrt{\frac{2\times 2.5\times {10}^{14}}{8.85\times {10}^{-12}\times 3\times {10}^8}} \\ \Rightarrow E_0=0.4339\times {10}^9 \\ \Rightarrow E_0=4.33\times {10}^8\mathrm{N}/\mathrm{C} \end{gathered}$$

Maximum value of magnetic field,
$$\begin{gathered} B_0=\frac{E_0}{c} \\ {B}_0=\frac{4.33\times {10}^8}{3\times {10}^8} \\ \Rightarrow B_0=1.43\mathrm{T} \end{gathered}$$