Q82 / 90 · JEE Main 2014 (06 Apr) · Physics

During the propagation of electromagnetic wave in a particular medium :-

A
Electric energy density is double of the magnetic energy density
B
Electric energy density is half of the magnetic energy density
Correct answer
C
Electric energy density is equal to the magnetic energy density
D
Both electric and magnetic energy densities are zero

Solution

${(\frac{U}{V})}_{elec} = \frac{1}{2} \in_{0} E^{2}$       ....(i)

${(\frac{U}{V})}_{mag} = \frac{1}{2} B^{2} / μ_{0}$      ....(ii)

$B = \frac{E}{C}$ (for EMW)         ....(iii)

and $C = \frac{1}{\sqrt{μ_{0} ε_{0}}}$ .....(iv)

∴ devide eqⁿ (i) by (ii)

$\frac{{(U / V)}_{e l e c}}{{(U / V)}_{m a g}} = \frac{\frac{1}{2} ε_{0} E^{2}}{\frac{1}{2} B^{2} / μ_{0}}$

$= {(\frac{E}{B})}^{2} μ_{0} ε_{0}$

by using eq (iii) & (iv)

$= \frac{C^{2}}{C^{2}} = 1$

$\Rightarrow {(U / V)}_{e l e c .} = {(\frac{U}{V})}_{m a g}$

Hence, the correct answer is option: 'C'.

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