The energy associated with the electric field | vedclass

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(D) For an electromagnetic wave in free space,the energy density of the electric field is given by $U_E = \frac{1}{2} \varepsilon_0 E^2$.The energy de

Vedclass · Accepted Answer

$U_E = U_B$

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(D) For an electromagnetic wave in free space,the energy density of the electric field is given by $U_E = \frac{1}{2} \varepsilon_0 E^2$.The energy density of the magnetic field is given by $U_B = \frac{B^2}{2 \mu_0}$.Using the relation $B = \frac{E}{c}$ and $c^2 = \frac{1}{\mu_0 \varepsilon_0}$,we substitute $B$ into the expression for $U_B$:$U_B = \frac{(E/c)^2}{2 \mu_0} = \frac{E^2}{2 \mu_0 c^2}$.Substituting $c^2 = \frac{1}{\mu_0 \varepsilon_0}$:$U_B = \frac{E^2}{2 \mu_0 (1 / \mu_0 \varepsilon_0)} = \frac{1}{2} \varepsilon_0 E^2$.Therefore,$U_E = U_B$.

The energy associated with the electric field is $(U_E)$ and with the magnetic field is $(U_B)$ for an electromagnetic wave in free space. Then

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