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. $1.44\times {10}^8\text{N/C},4.34\text{T}$
• B. $4.34\text{N/C},1.44\text{T}$
• C. $4.34\times {10}^8\text{N/C},1.44\times {10}^{-2}\text{T}$
• D. $4.34\times {10}^8\text{N/C},1.44\text{T}$

Answer 1

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

We know that formula for the intensity is given by:

$I=\frac{1}{2}{\epsilon }_0{E}^{2}c$

$\Rightarrow E=\sqrt{\frac{2I}{{\epsilon }_{0}c}}$

Here,

$I=2.5\times {10}^{14}{\text{W/m}}^2,{\epsilon }_0=8.85\times {10}^{-12}{\text{C}}^2/{\text{Nm}}^2$
$c=3\times {10}^8\text{m/s}$

$E=\sqrt{\frac{2\times 2.5\times {10}^{14}}{8.85\times {10}^{-12}\times 3\times {10}^8}}=4.34\times {10}^8\text{N/C}$

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, $\left(\text{D}\right)$ is the correct answer.