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Electromagnetic Waves question

2021 · 27 Jul · Shift 1 · Q50
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  5. /2021 · 27 Jul · Shift 1 · Q50

Electromagnetic Waves question

2021 · 27 Jul · Shift 1 · Q50

JEE MainPhysicsElectromagnetic WavesMCQ+4 / −1
The relative permittivity of distilled water is 81. The velocity of light in it will be : (Given μ\muμ r = 1)
  1. A
    4.33 ×\times× 107 m/s
  2. B
    2.33 ×\times× 107 m/s
  3. C
    3.33 ×\times× 107 m/s
  4. D
    5.33 ×\times× 107 m/s
View written solutionFree

Correct answer: C

  1. For an electromagnetic wave in a medium,

v=1μ εv = \frac{1}{\sqrt{\mu\,\varepsilon}}v=με​1​

Using relative values,

v=cμrεrv = \frac{c}{\sqrt{\mu_r\varepsilon_r}}v=μr​εr​​c​

  1. Given:

εr=81,μr=1\varepsilon_r = 81, \qquad \mu_r = 1εr​=81,μr​=1

So,

v=3×1081×81v = \frac{3\times 10^8}{\sqrt{1\times 81}}v=1×81​3×108​

  1. Compute the square root:

81=9\sqrt{81} = 981​=9

Therefore,

v=3×1089=0.333×108=3.33×107 m/sv = \frac{3\times 10^8}{9} = 0.333\times 10^8 = 3.33\times 10^7\ \text{m/s}v=93×108​=0.333×108=3.33×107 m/s

  1. Match with the options:
  • A: 4.33×1074.33\times 10^74.33×107 m/s
  • B: 2.33×1072.33\times 10^72.33×107 m/s
  • C: 3.33×1073.33\times 10^73.33×107 m/s
  • D: 5.33×1075.33\times 10^75.33×107 m/s

Hence, the correct option is C.

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