Question

A beam has intensity $2.5\times {10}^{14}W{m}^{-2}$. The ratio of electric and magnetic fields in the beam is

• A. $3.44T$
• B. $3.14T$
• C. $1.004T$
• D. $1.44T$

Answer 1

The correct option is D $1.44T$

$\begin{array}{c}I=2.5\times {10}^{14}W/m^2\\ Weknow,\\ I=\frac{1}{2}{e}_0{E}_0^{2}C\\ \Rightarrow E_0^2=\frac{2I}{e_{0}C}or{E}_0=\sqrt{\frac{2I}{e_{0}C}}\\ E_0=\sqrt{\frac{2\times 2.5\times {10}^{14}}{8.85\times {10}^{-12}\times 3\times {10}^8}}\\ =0.4339\times {10}^9=4.33\times {10}^{8}N/C.\\ B_0={\mu }_0{E}_{0}C{E}_0\\ =4\times 3.14\times {10}^{-7}\times 8.854\times {10}^{-12}\times 3\times {10}^8\times 4.33\times {10}^8\\ =1.44T\end{array}$

Hence, Option $D$ is correct .