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The electric field in an electromagnetic wave is given by E⃗ = ı̂ 40 cos(ω(t - z/c)) NC⁻¹. The magnetic field induction of this wave is (in SI unit)
Asked in JEE Main 4th April 1st Shift 2024 · Writing B from E, and E from B
- (1) B⃗ = k̂ (40)/c cos(ω(t - z/c))
- (2) B⃗ = ı̂ (40)/c cos(ω(t - z/c))
- (3) B⃗ = ȷ̂ 40 cos(ω(t - z/c))
- (4) B⃗ = ȷ̂ (40)/c cos(ω(t - z/c))
Answer: (4) B⃗ = ȷ̂ (40)/c cos(ω(t - z/c))
Step-by-step solution
ω(t - z/c) ⇒ the wave travels along +k̂; Ê = ı̂
B₀ = E₀/c = 40/c
k̂ = Ê × B̂ = ı̂ × B̂ ⇒ B̂ = ȷ̂
Why the other options are wrong
- (1) B along k̂ is the propagation direction; B must be perpendicular to it
- (2) B along ı̂ is parallel to E — the two fields are perpendicular
- (3) comes from the direction ȷ̂ is right, but you kept the amplitude 40 instead of 40/c
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