Question

A laser beam has intensity $2.5\times {10}^{14}{\text{Wm}}^{-2}$. The amplitudes of electric and magnetic fields in the beam are,

• A. $1.25\times {10}^8\text{N/C},4.34\text{T}$
• B. $4.34\times {10}^8\text{N/C},1.44\text{T}$
• C. $1.44\times {10}^8\text{N/C},4.34\text{T}$
• D. $4.34\text{N/C},1.44\text{T}$

Answer 1

The correct option is B $4.34\times {10}^8\text{N/C},1.44\text{T}$

We know that the intensity is given by,
$I=\frac{1}{2}{ϵ}_0{E}^{2}c$
$\Rightarrow E=\sqrt{\frac{2I}{{ϵ}_{0}c}}$

Here, $I=2.5\times {10}^{14}{\text{Wm}}^{-2}$
$c=3\times {10}^8\text{m/s}$
${ϵ}_0=8.85\times {10}^{-12}{\text{C}}^2/{\text{N-m}}^2$

$\Rightarrow E=\sqrt{\frac{2\times 2.5\times {10}^{14}}{8.85\times {10}^{-12}\times 3\times {10}^8}}$

$E=4.34\times {10}^8\text{N/C}$

The magnetic field is given by,
$B=\frac{E}{c}=\frac{4.34\times {10}^8}{3\times {10}^8}=1.44\text{T}$

Hence, $\left(C\right)$ is the correct answer.