Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →
Sign in

Electromagnetic Waves question

2023 · 31 Jan · Shift 1 · Q72
Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.
  1. PYQ Library
  2. /JEE Main
  3. /Physics
  4. /Electromagnetic Waves
  5. /2023 · 31 Jan · Shift 1 · Q72

Electromagnetic Waves question

2023 · 31 Jan · Shift 1 · Q72

JEE MainPhysicsElectromagnetic WavesNumerical+4 / −1
In a medium the speed of light wave decreases to 0.20.20.2 times to its speed in free space The ratio of relative permittivity to the refractive index of the medium is x:1x: 1x:1. The value of xxx is ‾\underline{\hspace{2cm}}​. (Given speed of light in free space =3×108 m s−1=3 \times 10^{8} \mathrm{~m} \mathrm{~s}^{-1}=3×108 m s−1 and for the given medium μr=1\mu_{\mathrm{r}}=1μr​=1)
Numerical answer
View written solutionFree

Correct answer: 5

  1. For an electromagnetic wave in a medium,

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

Given:

  • v=0.2cv = 0.2cv=0.2c
  • μr=1\mu_r = 1μr​=1

So,

0.2c=cεr0.2c = \frac{c}{\sqrt{\varepsilon_r}}0.2c=εr​​c​

Cancelling ccc,

0.2=1εr0.2 = \frac{1}{\sqrt{\varepsilon_r}}0.2=εr​​1​

εr=5\sqrt{\varepsilon_r} = 5εr​​=5

εr=25\varepsilon_r = 25εr​=25

  1. Refractive index of the medium is

n=cv=10.2=5n = \frac{c}{v} = \frac{1}{0.2} = 5n=vc​=0.21​=5

Also, since μr=1\mu_r=1μr​=1,

n=εr=5n = \sqrt{\varepsilon_r} = 5n=εr​​=5

  1. Required ratio is relative permittivity to refractive index:

εr:n=25:5=5:1\varepsilon_r : n = 25 : 5 = 5 : 1εr​:n=25:5=5:1

Hence,

x=5x = 5x=5

PreviousNext

More from Electromagnetic Waves

  • Match List I with List II Choose the correct answer from the options given below: Includes table2023 · MCQ
  • A plane electromagnetic wave travels in a medium of relative permeability 1.61 and relative permittivity 6.44. If magnitude of magnetic intensity is 4.5 × 10 − 2 Am − 1 at a point, what will be the approximate magnitude of…2022 · MCQ
  • An electric bulb is rated as 200 W. What will be the peak magnetic field at 4 m distance produced by the radiations coming from this bulb? Consider this bulb as a point source with 3.5% efficiency.2022 · MCQ
  • The rms value of conduction current in a parallel plate capacitor is 6.9μA. The capacity of this capacitor, if it is connected to 230 V ac supply with an angular frequency of 600rad/s,…2022 · MCQ
  • Light wave travelling in air along x-direction is given by Ey​=540sinπ×104(x−ct)Vm−1. Then, the peak value of magnetic field of wave will be (Given c = 3 × 108 ms − 1)2022 · MCQ
  • The electric field in an electromagnetic wave is given by E = 56.5 sin ω(t − x/c) NC − 1. Find the intensity of the wave if it is propagating along x-axis in the free space. (Given : ε 0 = 8.85 × 10 − 12C2N −…2022 · MCQ
  • The electromagnetic waves travel in a medium at a speed of 2.0 × 108 m/s. The relative permeability of the medium is 1.0. The relative permittivity of the medium will be :2022 · MCQ
  • The magnetic field of a plane electromagnetic wave is given by : B=2×10−8sin(0.5×103x+1.5×1011t)j^​ T. The amplitude of the electric…2022 · MCQ