Directions of E, B and Propagation: The E × B Rule
Physics · Electromagnetic Waves · NEET
In every electromagnetic wave the electric field E, the magnetic field B, and the direction the wave travels are all at 90° to each other (mutually perpendicular). The wave always moves along the direction of E × B (E cross B). Memory hook: point your right-hand fingers along E, curl them toward B, and your thumb points where the wave goes — this is the same order as x → y → z, so x̂ × ŷ = ẑ.
E (red) and B (blue, dashed) oscillate in the same phase but in perpendicular planes; the wave travels along E × B, which follows the right-hand cycle x̂ × ŷ = ẑ.
Your doubts, answered
Are E and B parallel or perpendicular to each other?
They are perpendicular (at 90°). In an EM wave, E and B are always at right angles to each other AND both are at right angles to the direction the wave moves. A quick check: E·B = 0 always. If a question gives you E and B that are parallel, that combination is not a valid EM wave.
Which cross product gives the direction of travel — E × B or B × A?
The wave travels along E × B (E cross B), in that exact order. E × B always points the way the wave goes. Note the order matters: B × E would point backward. So write it as (direction of E) × (direction of B) = direction of propagation.
How do I use the right-hand rule here?
Point the fingers of your right hand along E. Curl them toward B (through the smaller 90° angle). Your thumb now points in the direction the wave travels. Using unit vectors it follows the cycle x̂ × ŷ = ẑ, ŷ × ẑ = x̂, ẑ × x̂ = ŷ. Keep that cycle in mind and you never make a sign mistake.
If E is along +y and the wave moves along +x, where is B?
We need E × B along +x. Since E is along ŷ, we ask: ŷ × (?) = x̂. Because ŷ × ẑ = x̂, B must be along +z. So E along +y, wave along +x gives B along +z. (This is exactly NEET 2018.)
Are E and B in step or out of step (phase)?
They are in the same phase. Both reach their maximum at the same instant and both become zero at the same instant, at the same point. So if E = E0 sin(kx − ωt), then B = B0 sin(kx − ωt) with the same sign inside the bracket. They never point 'opposite in time' — only in space are they perpendicular.
Does the wave direction reverse if the phase is (kx + ωt) instead of (kx − ωt)?
Yes. A minus sign, (kx − ωt), means the wave travels along +x. A plus sign, (kx + ωt), means it travels along −x. Always read the sign inside the bracket first to fix the propagation direction, then apply E × B to place the fields correctly (NEET 2025 tests exactly this).
⚠️ The NEET trap ✗ Taking the wave direction as B × E, or assuming E and B are parallel, or forgetting that a (kx + ωt) sign flips the travel direction. ✓ Wave direction = E × B (this exact order). E ⊥ B ⊥ propagation, all mutually perpendicular, and E, B are in the same phase. Read the sign in (kx ∓ ωt) to fix travel direction first. 🧠 Order is everything: E first, B second, thumb = travel. Same cycle as x → y → z.
Real NEET questions
NEET 2018
An EM wave is propagating in a medium with velocity V = V î (along +x). The instantaneous oscillating electric field of this EM wave is along the +y axis. Then the direction of the oscillating magnetic field of the EM wave will be along
A · −y direction
B · +z direction ✓
C · −z direction
D · −x direction
Solution: Step 1: The wave travels along E × B, so E × B must point along +x (î). Step 2: E is given along +y (ĵ). Let B be along the unknown direction. We need ĵ × B̂ = î. Step 3: From the cyclic rule ŷ × ẑ = x̂, so B̂ = ẑ (+z). Answer: +z direction (B).
NEET 2021
For a plane electromagnetic wave propagating in the +x-direction, which one of the following combinations gives a correct possible pair of directions for the electric field (E) and magnetic field (B) respectively?
A · +ĵ−k̂ , −ĵ−k̂
B · −ĵ+k̂ , −ĵ+k̂
C · +ĵ+k̂ , ĵ+k̂
D · −ĵ+k̂ , −ĵ−k̂ ✓
Solution: Step 1: Two conditions must hold — E ⊥ B (so E·B = 0) and E × B along +x (î). Step 2: Test option D. E = −ĵ+k̂, B = −ĵ−k̂. Dot product: (−ĵ+k̂)·(−ĵ−k̂) = (+1) + (−1) = 0, so they are perpendicular. Step 3: Cross product E × B = (−ĵ+k̂) × (−ĵ−k̂). Expanding gives a vector along +î (the ĵ and k̂ terms combine to point along +x). Both conditions satisfied. Answer: (D).
NEET 2025
The electric field in a plane electromagnetic wave is given by E_z = 60 cos(5x + 1.5×10⁹ t) V/m. Then the expression for the corresponding magnetic field is (subscripts denote field direction)
A · B_z = 60 cos(5x + 1.5×10⁹ t) T
B · B_z = 60 sin(5x + 1.5×10⁹ t) T
C · B_y = 2×10⁻⁷ cos(5x + 1.5×10⁹ t) T ✓
D · B_x = 2×10⁻⁷ cos(5x + 1.5×10⁹ t) T
Solution: Step 1 (amplitude): B0 = E0/c = 60/(3×10⁸) = 2×10⁻⁷ T. Step 2 (travel direction): the phase is (5x + ωt) with a plus sign, so the wave moves along −x. Step 3 (B direction): E is along ẑ and propagation is along −x̂, so we need E × B along −x̂, i.e. ẑ × B̂ = −x̂. Since ẑ × ŷ = −x̂, B is along +y. Step 4: B stays in phase with E (same cos term). Result: B_y = 2×10⁻⁷ cos(5x + 1.5×10⁹ t) T. Answer: (C).
Solved Electromagnetic Waves NEET PYQs
Try the real previous-year questions from this chapter — each with the answer and a full solution.
An EM wave always travels in the direction of E × B, and E, B and the direction of travel are mutually perpendicular.
Are E and B perpendicular in an EM wave?
Yes, always. E ⊥ B, and both are perpendicular to the direction the wave moves. E·B = 0 at every point and instant.
Do E and B oscillate in phase?
Yes. They reach maximum and zero at the same time at any given point. If E = E0 sin(kx − ωt), then B = B0 sin(kx − ωt) with the same sign inside the bracket.
How do I find the direction the wave travels from its equation?
Look at the sign inside the bracket. (kx − ωt) means travel along +x; (kx + ωt) means travel along −x. The same logic applies for y and z.
Why is the wave direction E × B and not B × E?
By convention and by Maxwell's equations, the Poynting vector S = E × B points along energy flow, which is the direction of propagation. B × E would give the opposite (wrong) direction.
