JEE Main 2021 · 16 March · morning · Single correct · +4 / −1

A plane electromagnetic wave of frequency 500 MHz is travelling in vacuum along y-direction. At a particular point in space and time,
B⃗ = 8.0 × 10⁻⁸ zT. The value of electric field at this point is :
(speed of light = 3 × 10⁸ ms⁻¹)
x, y, z are unit vectors along x, y and z directions.

  1. (a) 2.6 x V/m
  2. (b) -24 x V/m
  3. (c) 24 x V/m
  4. (d) -2.6 y V/m
Answer and solution

Answer (b) -24 x V/m

Solution

Physics sir · 4 steps

Size from E = cB, sign from making E⃗ × B⃗ point along the travel direction.

  1. Magnitude. In vacuum the field magnitudes are tied by E = cB. The frequency does not enter this at all.

    E = cB = (3 × 10⁸)(8.0 × 10⁻⁸) = 24 V m⁻¹

  2. Direction. E⃗ and B⃗ are perpendicular to each other and to the travel direction, so E⃗ lies along ±x. The wave travels along E⃗ × B⃗, which must be +y.
  3. Check the sign. x × z = -y, which is the wrong way. (-x) × z = +y, which is correct, so E⃗ points along -x.
  4. So. E⃗ = -24 x V/m, which is option (b).

The idea to keep. For any EM wave, E = cB gives the size, and E⃗ × B⃗ must point along the direction of travel. Use that cross product to pick the sign.

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 2021.