Why Electric and Magnetic Fields Carry Equal Energy in an EM Wave
Physics · Electromagnetic Waves · NEET
In an electromagnetic wave, the energy stored in the electric field is always equal to the energy stored in the magnetic field. This happens because B = E/c and c = 1/sqrt(mu0 x eps0), which makes the electric energy density u_E = (1/2) eps0 E^2 exactly equal to the magnetic energy density u_B = B^2 / (2 mu0). Memory hook: "E and B are equal partners" — they split the wave's energy 50-50, so total u = eps0 E^2 = B^2 / mu0.
E and B oscillate in phase; using B = E/c and c = 1/sqrt(mu0 eps0), the electric energy density (1/2)eps0 E^2 exactly equals the magnetic energy density B^2/(2 mu0), so the wave's energy splits 50-50.
Your doubts, answered
Are the electric and magnetic energies really equal at every instant?
Yes. The electric energy density is u_E = (1/2) eps0 E^2 and the magnetic energy density is u_B = B^2 / (2 mu0). In an EM wave E and B oscillate in phase, and at every point B = E/c. Substituting B = E/c into u_B and using c^2 = 1/(mu0 eps0) gives u_B = (1/2) eps0 E^2 = u_E. Because they are equal at each instant, their time averages are also equal.
If they are equal, why do we bother writing both terms?
The total energy density is u = u_E + u_B. Since u_E = u_B, you can write u = eps0 E^2 = B^2 / mu0, or in terms of RMS values u_avg = (1/2) eps0 E0^2 = eps0 E_rms^2. Knowing the two halves are equal is a shortcut: compute one, double it.
What is the ratio of the electric to the magnetic contribution to intensity?
It is 1 : 1. Intensity is average energy flux, and half comes from the electric field and half from the magnetic field. NEET 2020 asked exactly this and the answer is D, 1:1. Do not fall for options like 1:c or c:1 — those confuse fields with energies.
B is a tiny number (like 10^-8 T) and E is a few V/m. How can their energies be equal?
The magnetic energy density has B^2 divided by a very small mu0 (4 pi x 10^-7), which boosts it. The electric term has E^2 multiplied by a very small eps0 (8.85 x 10^-12), which shrinks it. The two small constants and the factor c exactly cancel, so the numbers come out equal even though E and B look very different in size.
Does this equality hold inside a medium too?
The same structure holds, but you replace eps0 with eps = eps_r eps0 and mu0 with mu = mu_r mu0, and B = E/v with v = 1/sqrt(mu eps). The electric and magnetic energy densities are still equal to each other in a non-absorbing medium.
⚠️ The NEET trap ✗ Students think the electric field carries most of the energy because E (a few V/m) looks much bigger than B (about 10^-8 T), so they pick a ratio like c:1 or 1:c. ✓ Energy density uses E^2 with eps0 and B^2 with 1/mu0, not E and B directly. After using B = E/c, the two energy densities are exactly equal, so the ratio of contributions is 1:1. 🧠 Compare energies, not raw field values — E and B always split the energy 50-50.
Real NEET questions
2020
The ratio of contributions made by the electric field and magnetic field components to the intensity of an electromagnetic wave is (c = speed of electromagnetic waves)
A · 1 : c
B · 1 : c^2
C · c : 1
D · 1 : 1 ✓
Solution: Intensity is the average energy flux. Average electric energy density u_E = (1/2) eps0 E_rms^2 and average magnetic energy density u_B = B_rms^2 / (2 mu0). Using B = E/c and c^2 = 1/(mu0 eps0): u_B = E_rms^2 / (2 mu0 c^2) = (1/2) eps0 E_rms^2 = u_E. Since both halves are equal, their contributions to intensity are equal, giving the ratio 1 : 1. Answer: D.
2024
The property which is NOT of an electromagnetic wave travelling in free space is that
A · The energy density in the electric field is equal to the energy density in the magnetic field
B · They travel with a speed equal to 1/sqrt(mu0 eps0)
C · They originate from charges moving with uniform speed ✓
D · They are transverse in nature
Solution: Check each true property: (A) is TRUE — u_E = u_B is exactly this concept. (B) is TRUE — c = 1/sqrt(mu0 eps0). (D) is TRUE — EM waves are transverse. (C) is FALSE, because EM waves originate from ACCELERATING charges, not charges moving at uniform speed (a uniform-velocity charge does not radiate). The property that is NOT correct is C. Answer: C.
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 formula that proves electric and magnetic energy are equal?
u_E = (1/2) eps0 E^2 and u_B = B^2 / (2 mu0). Put B = E/c and c = 1/sqrt(mu0 eps0), and both reduce to (1/2) eps0 E^2, so u_E = u_B.
What is the total energy density of an EM wave?
u = u_E + u_B = 2 u_E = eps0 E^2 = B^2 / mu0. The average value is u_avg = (1/2) eps0 E0^2 = eps0 E_rms^2.
Is the ratio of electric to magnetic energy contribution 1:1?
Yes. This was directly asked in NEET 2020, and the correct answer is 1:1 (option D).
Does a charge moving at constant velocity produce an EM wave?
No. Only an accelerating (or oscillating) charge radiates an EM wave. This is why option C in NEET 2024 is the property that does NOT belong to an EM wave.
Why does B look so small compared to E but still store equal energy?
Because B = E/c and c is huge (3 x 10^8), B is tiny. But the magnetic energy uses B^2 / (2 mu0) with a very small mu0, which scales it back up to exactly match the electric part.
