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JEE Main2014PhysicsElectromagnetic WavesActual

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:

Options

  1. A1.34 ~V / m
  2. B2.68 ~V / m
  3. C4.02 ~V / m
  4. D5.36 ~V / m

Correct answer

B. 2.68 ~V / m

Step-by-step solution

Wavelength of monochromatic green light aligned &=5.5 10⁻⁵ ~cm & Intensity I = Power Area &= 100 (3 / 100) 4 (5)^2 &= 3 100 Wm ⁻² aligned Now, half of this intensity (I) belongs to electric field and half of that to magnetic field, therefore, aligned & I 2 = 1 4 ₀ E ₀^2 C & or E ₀= 2 I ₀ C aligned aligned &= 2 ( 3 100 ) ( 1 4 9 10^9 ) (3 10^8 . &= 6 25 30 = 7.2 & E ₀=2.68 ~V / m aligned

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