A plane electromagnetic wave of frequency 100 MHz is travelling in vacuum along the x-direction. At a particular point in space and time, B⃗ = 2.0 × 10⁻⁸k̂T. (where, k̂ is unit vector along z-direction) What is E⃗ at this point?

Solution

Physics sir · 3 steps

Get the size from E = cB, then use E × B along x to fix the direction.

1. Magnitude. In vacuum the field amplitudes are linked by the speed of light. The frequency of 100 MHz does not enter this relation.

   E = cB = (3 × 10⁸ m s⁻¹)(2.0 × 10⁻⁸ T) = 6.0 V m⁻¹

2. Direction. E⃗ and B⃗ are perpendicular to each other and to the direction of travel. E⃗ × B⃗ points along the propagation direction, +î. With B⃗ along k̂, E⃗ must be along ĵ, because ĵ × k̂ = î.
3. So. E⃗ = 6.0 ĵ V/m, which is option (c).

The idea to keep. For any EM wave in vacuum, E = cB gives the size. E⃗, B⃗ and the direction of travel form a right-handed set, so E⃗ × B⃗ points where the wave goes.

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