Energy Density of EM Waves: Electric and Magnetic Contributions
Physics · Electromagnetic Waves · NEET
In an EM wave, energy is stored in both the electric and magnetic fields. The electric part is u_E = (1/2)ε0 E² and the magnetic part is u_B = B²/(2µ0). Because E = cB and c = 1/√(µ0 ε0), these two are always equal, so the total energy density is u = ε0 E² = B²/µ0. Memory hook: "E and B split the energy 50-50 in every EM wave."
In an EM wave the electric field (blue) and magnetic field (red) oscillate together. Using E = cB, their energy densities u_E = (1/2)ε0 E² and u_B = B²/(2µ0) are always equal, so total energy density u = ε0 E² = B²/µ0.
Your doubts, answered
Is the electric field energy density bigger than the magnetic one, since E is a large number (like 6 V/m) and B is tiny (like 10⁻⁸ T)?
No. This is the most common trap. You cannot compare E and B directly because they carry different units. Put them in the energy formulas. u_E = (1/2)ε0 E² and u_B = B²/(2µ0). Substitute B = E/c and c² = 1/(µ0 ε0). Then u_B = (E/c)²/(2µ0) = E²/(2µ0 c²) = E² µ0 ε0 /(2µ0) = (1/2)ε0 E² = u_E. So even though E looks large and B looks small, the two energy densities come out exactly equal.
What is the total energy density formula I should remember?
Since u_E = u_B, the instantaneous total is u = u_E + u_B = 2 × (1/2)ε0 E² = ε0 E². You can also write it as u = B²/µ0. For the average total density over one cycle, use rms values: u_avg = (1/2)ε0 E0² = B0²/(2µ0), where E0 and B0 are the peak amplitudes.
Do I plug in peak value or rms value?
Depends on what the question asks. For instantaneous energy density at one moment, use the instantaneous E (or B) at that moment. For average energy density, use rms values: u_avg = ε0 E_rms² = (1/2)ε0 E0². Watch the (1/2): average of E² over a cycle is (1/2)E0², so u_avg = (1/2)ε0 E0² for the total.
Is energy density the same as intensity?
No. Energy density u is energy stored per unit volume (units J/m³). Intensity I is energy flowing per unit area per unit time (units W/m²). They are linked by I = u × c, because the stored energy travels at speed c. NEET sometimes asks the ratio of E and B contributions to intensity, which is still 1:1 because u_E = u_B.
Why do E and B carry equal energy?
Because in an EM wave they are locked together by E = cB at every instant. This relation, combined with c = 1/√(µ0 ε0), forces (1/2)ε0 E² and B²/(2µ0) to be equal. It is a direct result of Maxwell's equations, not a coincidence.
⚠️ The NEET trap ✗ Comparing the raw numbers E and B and concluding the electric field stores far more energy because E ≈ 6 while B ≈ 10⁻⁸. ✓ E and B have different units and cannot be compared directly. Once put into u_E = (1/2)ε0 E² and u_B = B²/(2µ0), they are exactly equal, so each contributes 50% and the ratio is 1:1. 🧠 Never compare E and B by their size. Compare their energy densities, and they are always equal.
Real NEET questions
NEET 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 : c²
C · c : 1
D · 1 : 1 ✓
Solution: Step 1: Write both energy densities. Electric: u_E = (1/2)ε0 E². Magnetic: u_B = B²/(2µ0). Step 2: Use the wave relation E = cB, so B = E/c. Then u_B = (E/c)²/(2µ0) = E²/(2µ0 c²). Step 3: Use c² = 1/(µ0 ε0), so 1/c² = µ0 ε0. Then u_B = E² (µ0 ε0)/(2µ0) = (1/2)ε0 E². Step 4: So u_E = u_B exactly. Since intensity contribution is proportional to energy density, the ratio is 1 : 1. Answer: D.
NEET 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/√(µ0 ε0)
C · They originate from charges moving with uniform speed ✓
D · They are transverse in nature
Solution: Check each. (A) True: u_E = (1/2)ε0 E² equals u_B = B²/(2µ0) because E = cB — a confirmed property. (B) True: EM waves travel at c = 1/√(µ0 ε0). (D) True: EM waves are transverse (E and B perpendicular to propagation). (C) False: EM waves are radiated only by accelerating charges, not by charges moving at uniform speed. So the property that is NOT true 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 energy density of an electromagnetic wave?
It is the electromagnetic energy stored per unit volume. Total instantaneous value is u = ε0 E² = B²/µ0, split equally between the electric part u_E = (1/2)ε0 E² and the magnetic part u_B = B²/(2µ0).
Are the electric and magnetic energy densities equal?
Yes. Because E = cB and c = 1/√(µ0 ε0), the two expressions (1/2)ε0 E² and B²/(2µ0) are always equal at every instant, so each carries half the total energy.
What is the average energy density of an EM wave?
Using rms values, u_avg = (1/2)ε0 E0² = B0²/(2µ0), where E0 and B0 are the peak amplitudes. The factor 1/2 comes from averaging sin² over one cycle.
How is energy density related to intensity?
Intensity I equals energy density times wave speed: I = u × c. The average intensity is I_avg = (1/2)ε0 c E0². Energy density is per unit volume (J/m³); intensity is per unit area per second (W/m²).
Why can't I say E stores more energy than B because E is a bigger number?
Because E and B have different units. Only after inserting them into their energy-density formulas can you compare them, and then they turn out exactly equal.
