JEE Main 2020 · 6 September · evening · Single correct · +4 / −1

For a plane electromagnetic wave, the magnetic field at a point x and time t is
B⃗ ( x,t ) = [ 1.2 × 10⁻⁷sin ( 0.5 × 10³x + 1.5 × 10¹¹t )k̂ ] T
The instantaneous electric field E⃗ corresponding to B⃗ is :
(speed of light c = 3 × 10⁸ ms –1 )

  1. (a) E⃗ ( x,t ) = [ 36 sin ( 1 × 10³x + 1.5 × 10¹¹t )î ] V/m
  2. (b) E⃗ ( x,t ) = [ 36 sin ( 0.5 × 10³x + 1.5 × 10¹¹t )k̂ ]V/m
  3. (c) E⃗ ( x,t ) = [ 36 sin ( 1 × 10³x + 0.5 × 10¹¹t )ĵ ]V/m
  4. (d) E⃗ ( x,t ) = [ - 36 sin ( 0.5 × 10³x + 1.5 × 10¹¹t )ĵ ]V/m
Answer and solution

Answer (d) E⃗ ( x,t ) = [ - 36 sin ( 0.5 × 10³x + 1.5 × 10¹¹t )ĵ ]V/m

Solution

Physics sir · 4 steps

Size from E₀ = cB₀, direction from E⃗ × B⃗ pointing along the wave's travel.

  1. Direction of travel. The phase is kx + ω t with a plus sign, so the wave moves along -x. Also ω / k = (1.5 × 10¹¹)/(0.5 × 10³) = 3 × 10⁸ m s⁻¹ = c. The electric field must have the same k and ω.
  2. Amplitude. E₀ = cB₀ = 3 × 10⁸ × 1.2 × 10⁻⁷ = 36 V m⁻¹.
  3. Direction of E. E⃗ × B⃗ must point along the direction of travel, -î. Since B⃗ is along +k̂, this needs E⃗ along -ĵ.

    (-ĵ) × k̂ = -(ĵ × k̂) = -î

  4. So. E⃗ = -36 sin(0.5 × 10³ x + 1.5 × 10¹¹ t)ĵ V m⁻¹, which is option (d).

The idea to keep. In an EM wave, E⃗ and B⃗ share the same phase, with E₀ = cB₀. One rule fixes their directions: E⃗ × B⃗ points the way the wave travels.

Answer from the NTA final answer key. Solution by PrepWiser.

Study Electromagnetic Waves

Asked about 130 times in JEE Main since 2020. This question is from 2020.