Question

The energy associated with electric field is $\text{(}{U}_E)$ and with magnetic fields is $\left(U_B\right)$ for an electromagnetic wave in free space. Then

• A. $U_E<U_B$
• B. $U_E=\frac{U_B}{2}$
• C. $U_E>U_B$
• D. $U_E=U_B$

Answer 1

The correct option is D $U_E=U_B$

Average energy density of magnetic field,
$U_B=\frac{B_0^2}{4{\mu }_0}$
Average density of electric field,
$U_E=\frac{{\epsilon }_0{E}_0^2}{4}$
Now, $E_0=C{B}_0\text{and}{C}^2=\frac{1}{{\mu }_0{ϵ}_0}$
$U_E=\frac{{\epsilon }_0}{4}\times C^2{B}_0^2=\frac{{\epsilon }_0}{4}\times \frac{1}{{\mu }_0{\epsilon }_0}\times B_0^2=\frac{B_0^2}{4{\mu }_0}=U_B$
$\therefore U_E=U_B$
Since energy density of electric and magnetic field is same, so energy associated with equal volume will be equal i.e., $U_E=U_B$