Question

The total energy density for an electromagnetic wave in vacuum is:

• A. ${\epsilon }_0\frac{E^2}{3}$
• B. ${\epsilon }_0{E}^2$
• C. $\frac{{\epsilon }_0{E}^2}{2}$
• D. $\frac{E^2}{{\epsilon }_0}$

Answer 1

The correct option is B ${\epsilon }_0{E}^2$

Energy density in electric field is $\frac{{\epsilon }_o{E}^2}{2}$
Energy density in magnetic field is $\frac{B^2}{2\mu }$
Total energy density is $\frac{\epsilon E^2}{2}+\frac{B^2}{2\mu }$

But $B=cE=\frac{E}{\sqrt{\mu {\epsilon }_o}}$
Substituting, total energy density is ${\epsilon }_0{E}^2$