An electromagnetic wave of frequency 1 × 1014 hertz is propagating along z - axis. The amplitude of electric field is 4 V/m. If ε 0 = 8.8 × 10 - 12 C2/N-m2, then average energy density of electric field will be: (a) 35.2 × 10 - 10 J/m3 (b) 35.2 × 10 - 11 J/m3 (c) 35.2 × 10 - 12 J/m3 (d) 35.2 × 10 - 13 J/m3

Answer: (c). Average electric energy density uE = 1/4ε₀ E₀² (frequency is not needed). uE = 1/4 × 8.8 × 10⁻¹² × 16 = 35.2 × 10⁻¹² J/m ³ So the answer is (c) 35.2 × 10⁻¹² J/m ³.

An electromagnetic wave of frequency 1 × 1014 hertz is propagating… | JEE Main 2014 (11 Apr, Shift 1)

Q34JEE Main 2014 · 11 APR · SHIFT 1Easy

Energy Density & Intensity

An electromagnetic wave of frequency 1 $\times$ 1014 hertz is propagating along z - axis. The amplitude of electric field is 4 V/m. If $\varepsilon$ 0 = 8.8 $\times$ 10 $-$ 12 C2/N-m2, then average energy density of electric field will be:

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Answer: (c)

Average electric energy density $\langle u_E \rangle = \tfrac{1}{4}\varepsilon_0 E_0^2$ (frequency is not needed).
$\langle u_E \rangle = \tfrac{1}{4} \times 8.8 \times 10^{-12} \times 16 = 35.2 \times 10^{-12}$ J/m $^3$
So the answer is (c) $35.2 \times 10^{-12}$ J/m $^3$ .

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