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JEE Main
Exam
JEE Main
Subject
Physics
Chapter
Electromagnetic Waves

JEE Main · Physics · Electromagnetic Waves

A 100W electric bulb produces electromagnetic radiation with...

A 100W100W electric bulb produces electromagnetic radiation with electric field amplitude of~2Vm−12Vm^{- 1} at a distance of 10m10m. Assuming it as a point source, estimate the efficiency of the bulb.

Options

  1. A4.94 . 9 %
  2. B2.52 . 5 %
  3. C13.313 . 3 %
  4. D19.719 . 7 %

Correct answer

C. 13.313 . 3 %

Step-by-step solution

Intensity =power×ηA...(1)= \dfrac{power \times η}{A} . . . \left(1\right)

We know,

\dfrac{1}{2}I=I =\dfrac{1}{2}{ε}_{0}E2cE^{2}c

I = \left(8 . 854 \times {10}^{- 12}\right) \left({2}^{2}\right) \left(3 \times {10}^{8}\right)</p><p>I = 0 . 0106wm^{- 2} . . . \left(2\right)

On substituting \left(2\right) in \left(1\right),~

0.0106=0 . 0106 =\dfrac{100 \times η}{4 \times \pi \times \left({10}^{2}\right)}

⇒η=0.133=13.3⇒ η = 0 . 133 = 13 . 3 %

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