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For an electromagnetic wave traveling in free space ....

For an electromagnetic wave traveling in free space, the relation between average energy densities due to electric $(U_e)$ and magnetic $(U_m)$ fields is:

(A) $U_e > U_m $         
(B) $U_e = U_m $
(C) $U_e \neq U_m $     
(D) $U_e < U_m $

Solution

We have, ${U_e} = \frac{1}{2}{ \in _0}{E^2}$ and ${U_m} = \frac{1}{2}\frac{{{B^2}}}{{{\mu _0}}}$

$\therefore \frac{{{U_e}}}{{{U_m}}} = {\mu _0}{ \in _0} \times \frac{{{E^2}}}{{{B^2}}}$

Using $\frac{E}{B} = c = \frac{1}{{\sqrt {{\mu _0}{ \in _0}} }}$,

$\frac{{{U_e}}}{{{U_m}}} = \frac{1}{{{c^2}}} \times {c^2} = 1$

Answer: (B)

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