Question

An electromagnetic wave passes through space and its equation is given by $E=E_0\sin (\omega t-kx)$ where $E$ is electric field. Energy density of electromagnetic wave in space is

• A. $\frac{1}{2}{\epsilon }_0{E}_0^2$
• B. $\frac{1}{4}{\epsilon }_0{E}_0^2$
• C. ${\epsilon }_0{E}_0^2$
• D. $2{\epsilon }_0{E}_0^2$

Answer 1

Answer: (A)

$\frac{1}{2}{\epsilon }_0{E}_0^2$

Energy density (EM waves) $={\epsilon }_0{E}_{rms}^2={\epsilon }_0{\left(\frac{E_0}{\sqrt{2}}\right)}^2=\frac{1}{2}{\epsilon }_0{E}_0^2$