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Electromagnetic Waves question

2020 · 8 Jan · Shift 2 · Q53
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Electromagnetic Waves question

2020 · 8 Jan · Shift 2 · Q53

JEE MainPhysicsElectromagnetic WavesMCQ+4 / −1
A plane electromagnetic wave of frequency 25 GHz is propagating in vacuum along the z-direction. At a particular point in space and time, the magnetic field is given by B→=5×10−8j^T\overrightarrow B = 5 \times {10^{ - 8}}\widehat jTB=5×10−8j​T. The corresponding electric field E→\overrightarrow EE is (speed of light c = 3 × 108 ms–1)
  1. A
    15 i^\widehat ii V / m
  2. B
    -15 i^\widehat ii V / m
  3. C
    1.66 × 10–16 i^\widehat ii V / m
  4. D
    -1.66 × 10–16 i^\widehat ii V / m
View written solutionFree

Correct answer: A

  1. Given data
  • Electromagnetic wave propagates along +z+z+z direction.
  • Magnetic field at the given point: B⃗=5×10−8 j^ T\vec B = 5\times 10^{-8}\,\hat j\ \text{T}B=5×10−8j^​ T
  • Speed of light: c=3×108 m s−1c=3\times 10^8\ \text{m s}^{-1}c=3×108 m s−1
  1. Relation between E⃗\vec EE, B⃗\vec BB, and direction of propagation

For an electromagnetic wave in vacuum, E=cBE = cBE=cB

Also, the direction of propagation is along: E⃗×B⃗\vec E \times \vec BE×B

Since the wave is propagating along +z+z+z, we need: E⃗×B⃗=+k^\vec E \times \vec B = +\hat kE×B=+k^

Given B⃗\vec BB is along +j^+\hat j+j^​, let E⃗=Exi^\vec E = E_x \hat iE=Ex​i^ Then, i^×j^=k^\hat i \times \hat j = \hat ki^×j^​=k^ So E⃗\vec EE must be along +i^+\hat i+i^.

Hence, direction of electric field is: E⃗∥+i^\vec E \parallel +\hat iE∥+i^

  1. Magnitude of electric field

Using E=cBE = cBE=cB E=(3×108)(5×10−8)E = (3\times 10^8)(5\times 10^{-8})E=(3×108)(5×10−8) E=15 V/mE = 15\ \text{V/m}E=15 V/m

  1. Write the vector form

Therefore, E⃗=15 i^ V/m\vec E = 15\,\hat i\ \text{V/m}E=15i^ V/m

  1. Check options
  • A: 15i^15\hat i15i^ V/m ✅
  • B: −15i^-15\hat i−15i^ V/m ❌ wrong direction
  • C: 1.66×10−16i^1.66\times 10^{-16}\hat i1.66×10−16i^ V/m ❌ wrong magnitude
  • D: −1.66×10−16i^-1.66\times 10^{-16}\hat i−1.66×10−16i^ V/m ❌ wrong magnitude and direction

Therefore, the correct option is A.

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