The rms value of the electric field of the light coming from the Sun is $720 \mathrm{~N} / \mathrm{C}$. The average total energy density of the electromagnetic wave is

(B) $4.58 \times 10^{-6} \mathrm{~J} / \mathrm{m}^{3}$

(A) $3.3 \times 10^{-3} \mathrm{~J} / \mathrm{m}^{3}$

(C) $6.37 \times 10^{-9} \mathrm{~J} / \mathrm{m}^{3}$

(D) $81.35 \times 10^{-12} \mathrm{~J} / \mathrm{m}^{3}$

JEE Main · 2006 · 30 Apr 2006 · Offline · EM Waves

The rms value of the electric field of the light coming from the Sun is

720 N / C

. The average total energy density of the electromagnetic wave is

(A) $3.3 \times 1 0^{- 3} J / m^{3}$
(B) $4.58 \times 1 0^{- 6} J / m^{3}$ ✓ Correct
(C) $6.37 \times 1 0^{- 9} J / m^{3}$
(D) $81.35 \times 1 0^{- 12} J / m^{3}$

Answer: (B)

Solution

The average energy density of an electromagnetic wave can be written in terms of the rms electric field as

u = ε_{0} E_{rms}^{2}

, the electric and magnetic parts contributing equally. With

E_{rms} = 720 N/C

u = 8.85 \times 1 0^{- 12} \times 72 0^{2} \approx 4.58 \times 1 0^{- 6} J/m^{3}

JEE Main · 2006 · 30 Apr 2006 · Offline · Single correct option

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