JEE Main 2020 · 9 January · evening · Single correct · +4 / −1
A plane electromagnetic wave is propagating along the direction (î + ĵ)/√2 , with its polarization along the direction k̂ . The correct form of the magnetic field of the wave would be (here B₀ is an appropriate constant) :
- (a) B₀(î - ĵ)/√2 cos ( ω t - k(î + ĵ)/√2 )
- (b) B₀(î + ĵ)/√2 cos ( ω t - k(î + ĵ)/√2 )
- (c) B₀(ĵ - î)/√2 cos ( ω t + k(î + ĵ)/√2 )
- (d) B₀k̂cos ( ω t - k(î + ĵ)/√2 )
Answer and solution
Answer (a) B₀(î - ĵ)/√2 cos ( ω t - k(î + ĵ)/√2 )
Solution
Physics sir · 4 steps
B must be perpendicular to both E and the travel direction, and E × B must point the way the wave moves.
- Two perpendicular rules. In an EM wave, B⃗ is perpendicular to the direction of travel n = (î+ĵ)/√2. It is also perpendicular to E⃗, which here is along k̂. So B⃗ lies in the x-y plane and is perpendicular to î+ĵ. That leaves the direction ±(î-ĵ)/√2.
- Fix the sign. The energy flows along E⃗ × B⃗, and this must point along n. Check k̂ × (î-ĵ) using k̂×î = ĵ and k̂×ĵ = -î.
k̂ × (î-ĵ)/√2 = (ĵ+î)/√2 = n
- Check the phase. A wave moving along +n has phase ω t - k n·r⃗, with a minus sign. A plus sign would mean the wave travels along -n.
- So. Option (a) has B⃗ along (î-ĵ)/√2 and the correct phase ω t - k n·r⃗. The answer is (a).
The idea to keep. For any EM wave, E, B and the propagation direction form a right-handed set: E × B points along the travel direction. Use that cross product to fix the direction of B.
Answer from the NTA final answer key. Solution by PrepWiser.