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JEE Main
Exam
JEE Main
Subject
Physics
Chapter
Electromagnetic Waves

JEE Main · Physics · Electromagnetic Waves

Assume that a lamp radiates power P uniformly in all directions....

Assume that a lamp radiates power PP uniformly in all directions. The magnitude of electric field strength at a distance rr from the lamp is

Options

  1. APπcε0r2\dfrac{P}{{πcε}_{0}r^{2}}
  2. BP2πcεr2\dfrac{P}{2{πcεr}^{2}}
  3. CP2πε0r2c\sqrt{\dfrac{P}{2{πε}_{0}r^{2}c}}
  4. DPπε0cr2\sqrt{\dfrac{P}{{πε}_{0}{cr}^{2}}}

Correct answer

C. P2πε0r2c\sqrt{\dfrac{P}{2{πε}_{0}r^{2}c}}

Step-by-step solution

Intensity, I=powerarea=P4πr2I = \dfrac{power}{area} = \dfrac{P}{4{πr}^{2}} = average energy density ×\times velocity=12ε0E02c= \dfrac{1}{2}{ε}_{0}{E}_{0}^{2}c

∴E0=2P4πε0r2c=P2πε0r2c∴ {E}_{0} = \sqrt{\dfrac{2P}{4{πε}_{0}r^{2}c}} = \sqrt{\dfrac{P}{2{πε}_{0}r^{2}c}}
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