Question

The energy associate with electric field is $\left(U_E\right)$ and with magnetic field is $\left(U_B\right)$ for an electromagetic wave in free space. Then :

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

Answer 1

Answer: (C)

$U_E=U_B$

Average energy density of magnetic field, $u_B=\frac{B_0^2}{2{\mu }_0},B_0$ is maximum value of magnetic
field.
Average energy density of electric field,
Average energy density of electric field,
$u_E=\frac{{\epsilon }_0{\in }_0^2}{2}$
now, ${\in }_0=C{B}_0,C^2=\frac{1}{{\mu }_0{\in }_0}$
${\mu }_E=\frac{{\in }_0}{2}\times C^2{B}_0^2$
$=\frac{{\in }_0}{2}\times \frac{1}{{\mu }_0{\in }_0}\times B_0^2=\frac{B_0^2}{2{\mu }_0}={\mu }_B$
$u_E=u_B$
since energy density of electric & magnetic
field is same, energy associated with equal
volume will be equal.
$u_E=u_B$