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JEE Main 2014 (12 Apr, Shift 1) · Energy Density & Intensity

Energy Density & Intensity question from JEE Main 2014 (12 Apr, Shift 1)

Q35JEE Main 2014 · 12 APR · SHIFT 1Medium

Energy Density & Intensity

A lamp emits monochromatic green light uniformly in all directions. The lamp is 3% efficient in converting electrical power to electromagnetic waves and consumes 100 W of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of 5 m from the lamp will be nearly:

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Answer: (b)

  1. Radiated power P=0.03×100=3 WP = 0.03 \times 100 = 3\ \text{W}
  2. I=34π×25≈9.55×10−3 W/m2I = \dfrac{3}{4\pi \times 25} \approx 9.55 \times 10^{-3}\ \text{W/m}^2
  3. E0=2Iε0c=2×9.55×10−32.655×10−3=7.19E_0 = \sqrt{\dfrac{2I}{\varepsilon_0 c}} = \sqrt{\dfrac{2 \times 9.55 \times 10^{-3}}{2.655 \times 10^{-3}}} = \sqrt{7.19}
  4. E0≈2.68 V/mE_0 \approx 2.68\ \text{V/m}, so the answer is (b).
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