An electromagnetic wave is transporting energy in the negative z direction. At a certain point and certain time the direction of electric field of the wave is along positive y direction. What will be the direction of the magnetic field of the wave at that point and instant?

Solution

Physics sir · 4 steps

The energy flows along E⃗ × B⃗, so find the B that turns +y into -z.

1. Transverse wave. In an EM wave, E⃗ and B⃗ are perpendicular to each other and to the direction of travel. Here the wave travels along z and E⃗ is along y, so B⃗ must lie along x.
2. Fix the sign. Energy is carried along E⃗ × B⃗ (the Poynting vector). This cross product must point along -k̂.

   ĵ × î = -k̂

3. Check the other choice. With B⃗ along -î you would get ĵ × (-î) = +k̂. That sends energy the wrong way, so it is ruled out.
4. So. The magnetic field points along the positive x direction, which is option (c).

The idea to keep. For any EM wave, E⃗ × B⃗ points along the direction of travel. Use the cyclic order î → ĵ → k̂ to fix the sign of the missing field.

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