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Electromagnetic Waves question

2018 · 16 Apr · Shift 1 · Q55
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Electromagnetic Waves question

2018 · 16 Apr · Shift 1 · Q55

JEE MainPhysicsElectromagnetic WavesMCQ+4 / −1
A plane electromagnetic wave of wavelength λ\lambdaλ has an intensity I. It is propagatting along the positive Y-direction. The allowed expressions for the electric and magnetic fields are givn by :
  1. A
    JEE Main 2018 (Online) 16th April Morning Slot Physics - Electromagnetic Waves Question 139 English Option 1
  2. B
    JEE Main 2018 (Online) 16th April Morning Slot Physics - Electromagnetic Waves Question 139 English Option 2
  3. C
    JEE Main 2018 (Online) 16th April Morning Slot Physics - Electromagnetic Waves Question 139 English Option 3
  4. D
    JEE Main 2018 (Online) 16th April Morning Slot Physics - Electromagnetic Waves Question 139 English Option 4
View written solutionFree

Correct answer: A

The question statement is incomplete: the field expressions for options A, B, C, and D are missing.

To determine which expressions are allowed for a plane electromagnetic wave propagating along the positive YYY-direction, we must check the following conditions for each option:

  1. Direction of propagation For a wave traveling along +Y+Y+Y, the phase must be of the form ky−ωtky-\omega tky−ωt (or any equivalent form such as ωt−ky\omega t-kyωt−ky inside sine/cosine).

  2. Mutual perpendicularity The electric field E⃗\vec EE and magnetic field B⃗\vec BB must be perpendicular to each other and also perpendicular to the direction of propagation. Since propagation is along y^\hat yy^​, both E⃗\vec EE and B⃗\vec BB must lie in the xzxzxz-plane.

  3. Right-hand rule / Poynting vector direction The propagation direction is given by S⃗∝E⃗×B⃗\vec S \propto \vec E \times \vec BS∝E×B so we need E⃗×B⃗=+y^.\vec E \times \vec B = +\hat y.E×B=+y^​.

  4. Magnitude relation For an electromagnetic wave, E0=cB0.E_0 = cB_0.E0​=cB0​.

  5. Intensity relation If intensity is III, then in vacuum I=12cε0E02=12cμ0B02.I = \frac{1}{2}c\varepsilon_0 E_0^2 = \frac{1}{2}\frac{c}{\mu_0}B_0^2.I=21​cε0​E02​=21​μ0​c​B02​.

Because the actual expressions in options A, B, C, and D are not provided, it is impossible to verify which one satisfies all these conditions.

So, although the stored correct answer is marked as A, I cannot independently confirm it from the given data.

If you send the missing field expressions for options A–D, I can evaluate them one by one and give the final verified answer.

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