JEE Main 2025 · 28 January · evening · Single correct · +4 / −1
The magnetic field of an E.M. wave is given by B⃗ = ( √3/2 î + 1/2 ĵ ) 30 sin [ ω ( t - z/c ) ] (S.I. Units).
The corresponding electric field in S.I. units is:
- (a) E⃗=(1/2 î+√3/2 ĵ) 30 c sin [ω(t+z/c)]
- (b) E⃗=(1/2 î-√3/2 ĵ) 30 c sin [ω(t-z/c)]
- (c) E⃗=(√3/2 î-1/2 ĵ) 30 c sin [ω(t+z/c)]
- (d) E⃗=(3/4 î+1/4 ĵ) 30 c cos [ω(t-z/c)]
Answer and solution
Answer (b) E⃗=(1/2 î-√3/2 ĵ) 30 c sin [ω(t-z/c)]
Solution
Physics sir · 4 steps
Find the direction first: E must be perpendicular to B, and E × B must point along the wave's motion, +z.
- Read the wave. The phase ω(t - z/c) means the wave moves along +k̂. In an EM wave, E⃗ and B⃗ oscillate in phase, so E⃗ must carry the same sin[ω(t - z/c)]. Its amplitude is E₀ = cB₀ = 30c.
- Direction of E. The vectors E⃗, B⃗ and k̂ form a right-handed set, so E⃗ = c B⃗ × k̂. Cross the unit vector of B⃗ with k̂, using î × k̂ = -ĵ and ĵ × k̂ = î.
(√3/2î + 1/2ĵ) × k̂ = 1/2î - √3/2ĵ
- Check it. The dot product with B⃗ is 1/2·√3/2 - √3/2·1/2 = 0, so the two fields are perpendicular. The z-component of E × B is 1/4 + 3/4 = 1, so the wave travels along +z as required.
- So. E⃗ = (1/2î - √3/2ĵ) 30c sin[ω(t - z/c)], which is option (b).
The idea to keep. For an EM wave, E⃗, B⃗ and the direction of travel form a right-handed set, the two fields stay in phase, and E₀ = cB₀. Check all three against every option.
Answer from the NTA final answer key. Solution by PrepWiser.