A plane electromagnetic wave is written as Ex = E0 sin(kx − ωt) and By = B0 sin(kx − ωt). The two fields are in step (same phase), point at right angles to each other, and travel together along +x. Memory hook: E and B "sing the same song" (same sin, same k, same ω) — only their directions and amplitudes differ, with B0 = E0/c.
E (blue, along y) and B (red dashed, along z) oscillate in the same phase but at right angles; both share k = 2π/λ and ω = 2πf, with B0 = E0/c, and E × B points along the +x travel direction.
Your doubts, answered
What does (kx − ωt) actually mean, and how do I read the direction of travel?
(kx − ωt) is the phase of the wave. The rule is simple: if x and t have OPPOSITE signs, the wave moves in the +x direction; if they have the SAME sign, it moves in the −x direction. So Ex = E0 sin(kx − ωt) travels along +x, while Ez = 60 cos(5x + ωt) travels along −x. Here k = 2π/λ is the wave number (how much phase per metre) and ω = 2πf is the angular frequency (how much phase per second).
Why are E and B in the same phase and not 90° apart?
In a travelling EM wave both fields grow and fall together: when E is maximum, B is also maximum; when E is zero, B is zero. This comes from Maxwell's equations, which lock a changing E to a changing B at every point. Do not confuse this with the fields being perpendicular in DIRECTION (E along y, B along z) — direction and phase are two different things. Same phase, perpendicular directions.
How do I write the B equation if only the E equation is given?
Keep the same sin/cos, same k, same ω, and same phase sign as the E equation. Only two things change: (1) the amplitude becomes B0 = E0/c, and (2) the direction must be perpendicular to E and chosen so that E × B points along the direction of travel. Example: for Ex = E0 sin(kx − ωt) travelling along +x with E along ... (E is along x here is a special notation issue — in NEET the field subscript is its direction). When E is along y, B is along z: By→ actually Bz = (E0/c) sin(kx − ωt).
Is k the same as the wavelength, and ω the same as the frequency?
No — they are related but not equal. k = 2π/λ, so wavelength λ = 2π/k. Similarly ω = 2πf, so frequency f = ω/(2π). A common NEET slip is to read the number in front of x as the wavelength; it is actually the wave number k. Also, wave speed comes out as v = ω/k, which in vacuum equals c.
Do E0 and B0 have the same numerical value?
No. Because B0 = E0/c and c ≈ 3 × 10^8 m/s, the magnetic amplitude is about 300 million times smaller than the electric amplitude in SI units. So if E0 = 48 V/m, then B0 = 48 / (3 × 10^8) = 1.6 × 10^−7 T. The small number for B0 is normal, not an error.
⚠️ The NEET trap ✗ Since Ex = E0 sin(kx − ωt) and By = B0 sin(kx − ωt) have the same sin term, E and B point the same way — so E × B is zero and there is no propagation. ✓ Same phase means they peak at the same instant, but their DIRECTIONS are perpendicular (E along y, B along z). E × B is maximum, not zero, and it points along the travel direction +x. Phase and direction are independent — read the subscript for direction, read the phase (kx − ωt) for timing and travel sense. 🧠 Same phase does NOT mean same direction.
Real NEET questions
2025
The electric field in a plane electromagnetic wave is given by Ez = 60 cos(5x + 1.5 × 10^9 t) V/m. Then the expression for the corresponding magnetic field is (subscripts denote field direction):
A · Bz = 60 cos(5x + 1.5 × 10^9 t) T
B · Bz = 60 sin(5x + 1.5 × 10^9 t) T
C · By = 2 × 10^−7 cos(5x + 1.5 × 10^9 t) T ✓
D · Bx = 2 × 10^−7 cos(5x + 1.5 × 10^9 t) T
Solution: Step 1 — Amplitude: B0 = E0/c = 60 / (3 × 10^8) = 2 × 10^−7 T. So options A and B (which keep 60) are wrong. Step 2 — Same function and phase: E used cos(5x + 1.5×10^9 t), so B must also be cos(5x + 1.5×10^9 t). Step 3 — Direction: the (5x + ωt) phase means the wave travels along −x. E is along z. B must be perpendicular to E and satisfy E × B pointing along −x. Working the E × B rule gives B along y. Therefore By = 2 × 10^−7 cos(5x + 1.5 × 10^9 t) T. Answer: C.
2026
An EM wave travelling in a lossless dielectric of dielectric constant εr = 9 has electric field Ex = E0 sin(kz − 2π × 10^6 t) V/m. Among the following, the INCORRECT choice is:
A · The speed of the EM wave inside the medium is 10^8 m/s
B · The wavelength of the EM wave inside the medium is 300 m ✓
C · The magnetic field is By = (B0/v) sin(kz − 2π × 10^6 t), where v is the wave speed in the medium
D · The direction of propagation of the EM wave is along +z
Solution: Read the equation Ex = E0 sin(kz − 2π×10^6 t). Step 1 — Direction: z and t have opposite signs, so the wave travels along +z (option D is correct). Step 2 — Speed: v = c/√εr = (3 × 10^8)/√9 = (3 × 10^8)/3 = 10^8 m/s (option A correct). Step 3 — Frequency: ω = 2π × 10^6, so f = 10^6 Hz. Wavelength λ = v/f = 10^8 / 10^6 = 100 m, NOT 300 m — so option B is the INCORRECT statement, and thus the answer. Note the trap: 300 m would be the vacuum wavelength (c/f = 3×10^8/10^6), not the wavelength inside the medium. Answer: B.
Solved Electromagnetic Waves NEET PYQs
Try the real previous-year questions from this chapter — each with the answer and a full solution.
What is the standard form of the EM wave equations for E and B?
For a wave along +x: Ey = E0 sin(kx − ωt) and Bz = B0 sin(kx − ωt), where k = 2π/λ, ω = 2πf, and B0 = E0/c. Both fields share the same phase and the same k and ω.
How do you find the direction of propagation from the equation?
Look at the signs of x and t in the phase. Opposite signs (kx − ωt) → wave moves along +x. Same signs (kx + ωt) → wave moves along −x.
Why is the magnetic amplitude B0 so small compared to E0?
Because B0 = E0/c and c ≈ 3 × 10^8 m/s. Dividing by such a large number makes B0 roughly 3 × 10^8 times smaller than E0, so B0 values look tiny (like 10^−7 or 10^−8 T).
What do k and ω represent physically?
k = 2π/λ is the wave number — the amount of phase change per metre of distance. ω = 2πf is the angular frequency — the phase change per second. Wave speed v = ω/k, which equals c in vacuum.
Are E and B always in the same phase in a travelling EM wave?
Yes, for a plane wave in free space or a lossless medium, E and B reach their peaks and zeros at the same instant. They differ only in direction (perpendicular) and amplitude (B0 = E0/c).
