The electric field in an electromagnetic wave is given as Where and are angular frequency and velocity of electromagnetic wave respectively. The energy contained in a volume of will be (Given ) [2023]

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Q.
The electric field in an electromagnetic wave is given as $\vec{E} = 20 \sin ω (t - \frac{x}{c}) \hat{j} {NC}^{- 1}$

Where $ω$ and $c$ are angular frequency and velocity of electromagnetic wave respectively. The energy contained in a volume of $5 \times 10^{- 4} m^{3}$ will be

(Given $ε_{0} = 8.85 \times 10^{- 12} C^{2} / {Nm}^{2}$ ) [2023]

1 $28.5 \times 10^{- 13} J$

2 $17.7 \times 10^{- 13} J$

3 $8.85 \times 10^{- 13} J$

4 $88.5 \times 10^{- 13} J$

Ans.
(3)

$\vec{E} = 20 \sin ω (t - \frac{x}{c}) \hat{j} {NC}^{- 1}$

$Average energy density of an EM wave = \frac{1}{2} ε_{0} E_{0}^{2}$

$Energy stored = (\frac{1}{2} ε_{0} E_{0}^{2}) (Volume)$

$= \frac{1}{2} \times 8.85 \times 10^{- 12} \times {(20)}^{2} \times (5 \times 10^{- 4}) J$

$= 8.85 \times 10^{- 13} J$

Solution

1 $28.5 \times 10^{- 13} J$

2 $17.7 \times 10^{- 13} J$

3 $8.85 \times 10^{- 13} J$

4 $88.5 \times 10^{- 13} J$

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Solution

Q. The electric field in an electromagnetic wave is given as E→=20sinω(t-xc)j^ NC-1 Where ω and c are angular frequency and velocity of electromagnetic wave respectively. The energy contained in a volume of 5×10-4 m3 will be (Given ε0=8.85×10-12 C2/Nm2) [2023]

1 28.5×10-13 J

2 17.7×10-13 J

3 8.85×10-13 J

4 88.5×10-13 J

Ans. (3) E→=20sinω(t-xc)j^ NC-1 Average energy density of an EM wave=12 ε0E02 Energy stored=(12 ε0E02)(Volume) =12×8.85×10-12×(20)2×(5×10-4) J =8.85×10-13 J

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1 $28.5 \times 10^{- 13} J$

2 $17.7 \times 10^{- 13} J$

3 $8.85 \times 10^{- 13} J$

4 $88.5 \times 10^{- 13} J$