In a plane electromagnetic wave, the electric field oscillates with a frequency 2 × 1010 s -1 and amplitude 40 Vm -1, then the energy density due to electric field is (ε0=8.85 × 10-12 Fm -1)

Question

In a plane electromagnetic wave, the electric field oscillates with a frequency 2 × 1010 s -1 and amplitude 40 Vm -1, then the energy density due to electric field is (ε0=8.85 × 10-12 Fm -1) (A)  1.52 × 10-9 Jm-3  (B)  2.54 × 10-9 Jm-3  (C)  3.54 × 10-9 Jm-3  (D)  4.56 × 10-9 Jm-3

Tardigrade Admin · Accepted Answer

Energy density due to electric field is U=(1/2) ε0 E2 Here, E=(E0/√2)=(40/√2) ∴ U=(1/2) × 8.85 × 10-12 × (40 × 40/2) = 3.54 × 10-9 J / m 3

Q. In a plane electromagnetic wave, the electric field oscillates with a frequency $2 \times 1 0^{10} s^{- 1}$ and amplitude $40 V m^{- 1}$ , then the energy density due to electric field is $(ε_{0} = 8.85 \times 1 0^{- 12} F m^{- 1})$

$1.52 \times 1 0^{- 9} J m^{- 3}$

$2.54 \times 1 0^{- 9} J m^{- 3}$

$3.54 \times 1 0^{- 9} J m^{- 3}$

$4.56 \times 1 0^{- 9} J m^{- 3}$

Energy density due to electric field is
$U = \frac{1}{2} ε_{0} E^{2}$
Here, $E = \frac{E _{0}}{2} = \frac{40}{2}$
$∴ U = \frac{1}{2} \times 8.85 \times 1 0^{- 12} \times \frac{40 \times 40}{2}$
$= 3.54 \times 1 0^{- 9} J / m^{3}$

Q. In a plane electromagnetic wave, the electric field oscillates with a frequency 2×1010s−1 and amplitude 40Vm−1, then the energy density due to electric field is (ε0​=8.85×10−12Fm−1)

1.52×10−9Jm−3

2.54×10−9Jm−3

3.54×10−9Jm−3

4.56×10−9Jm−3