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Speed of EM Waves: c = 1/√(µ0ε0) Formula and Meaning

Physics · Electromagnetic Waves · NEET

Every electromagnetic wave in vacuum travels at one fixed speed, c = 1/√(µ0ε0), where µ0 is the permeability of free space and ε0 is the permittivity of free space. Putting µ0 = 4π×10^-7 and ε0 = 8.85×10^-12 gives c ≈ 3×10^8 m/s, the speed of light. Memory hook: "mu-epsilon under the root, one over it gives light's route."
Speed of an EM wave in free spacex (propagation)E fieldB fieldc = 1 / √(µ0 ε0)= 3 × 10^8 m/s (same for ALL EM waves)
In vacuum, the E field (blue) and B field (red) oscillate together and the whole wave moves at c = 1/√(µ0ε0) ≈ 3×10^8 m/s. The speed depends only on µ0 and ε0, not on amplitude or frequency.

Your doubts, answered

Why does 1/√(µ0ε0) come out to 3×10^8 m/s?

Just substitute the constants. µ0 = 4π×10^-7 T·m/A and ε0 = 8.85×10^-12 C²/(N·m²). Then µ0ε0 = (4π×10^-7)(8.85×10^-12) ≈ 1.11×10^-17. Its square root is about 3.33×10^-9. Taking 1 divided by that gives c ≈ 3×10^8 m/s. So the speed of light is not an independent measured number here; it is fixed by the two basic electric and magnetic constants of empty space.

What do µ0 and ε0 physically mean?

ε0 (permittivity of free space) tells you how strongly electric fields form in vacuum, and it appears in Coulomb's law. µ0 (permeability of free space) tells you how strongly magnetic fields form in vacuum, and it appears in the law for the magnetic field of a current. Maxwell's big result was that these two purely electric and magnetic constants combine to give the speed of light, proving light is an electromagnetic wave.

Do all EM waves have the same speed c?

Yes, in vacuum. Radio waves, microwaves, visible light, X-rays and gamma rays all travel at the same c = 3×10^8 m/s in free space, because c = 1/√(µ0ε0) has no frequency term in it. They differ only in frequency and wavelength (c = fλ), not in speed. This is a favourite NEET fact.

Does wave speed depend on how bright or how fast-oscillating the wave is?

No. The formula c = 1/√(µ0ε0) contains only µ0 and ε0. It has nothing to do with amplitude (brightness/field strength) or frequency. So changing E0, B0 or the frequency does not change the speed in vacuum. Only entering a material medium changes the speed, and then you use v = 1/√(µε).

How is c = 1/√(µ0ε0) different from v = 1/√(µε)?

c = 1/√(µ0ε0) is the speed in vacuum (free space), using the free-space constants. v = 1/√(µε) is the speed inside a material medium, using that medium's actual µ and ε. Since µ = µ0µr and ε = ε0εr, you get v = c/√(µrεr), which is always less than or equal to c. Do not mix the two.

⚠️ The NEET trap
✗ Students see 'permeability' and 'permittivity' and write c = √(µ0ε0), or think a stronger field or higher frequency makes the wave faster.
✓ The constants sit UNDER a square root in the DENOMINATOR: c = 1/√(µ0ε0). Speed depends only on µ0 and ε0, never on amplitude or frequency. In vacuum every EM wave moves at 3×10^8 m/s.
🧠 One over root mu-epsilon. If you forget the '1 over', your answer collapses to ~10^-9 instead of 10^8 m/s.

Real NEET questions

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/√(µ0ε0)
C · They originate from charges moving with uniform speed ✓
D · They are transverse in nature
Solution: Check each statement. (A) True: in an EM wave u_E = u_B. (B) True: the speed in free space is exactly c = 1/√(µ0ε0) = 3×10^8 m/s. (D) True: EM waves are transverse (E and B perpendicular to propagation). (C) is FALSE: EM waves come from ACCELERATING charges, not charges moving at uniform (constant) speed. A uniformly moving charge gives a steady current and no radiation. So the property that is NOT correct is (C).
NEET 2023 Phase 2

ε0 and µ0 are the electric permittivity and magnetic permeability of free space. If the corresponding quantities of a medium are 2ε0 and 1.5µ0, the refractive index of the medium will nearly be:

A · 3
B · 2
C · √2
D · √3 ✓
Solution: Speed in vacuum: c = 1/√(µ0ε0). Speed in medium: v = 1/√(µε) = 1/√((1.5µ0)(2ε0)) = 1/√(3 µ0ε0). Refractive index n = c/v = √(µ0ε0 × 3 µ0ε0) ÷ (µ0ε0) — simpler: n = c/v = √(3) because n = √(µr εr) = √(1.5 × 2) = √3. So n = √3.

Solved Electromagnetic Waves NEET PYQs

Try the real previous-year questions from this chapter — each with the answer and a full solution.

See all 20 Electromagnetic Waves NEET PYQs ›
Next concept: Ratio E0/B0 = c →Keep learning — 2 minFeeling ready? Solve the Electromagnetic Waves NEET PYQs ›Or practice on your phone — get the free MedicNEET app ›

Frequently asked

Is the speed of light a fundamental constant or derived from µ0 and ε0?

In the classical Maxwell picture it is derived: c = 1/√(µ0ε0). Because µ0 and ε0 are fixed constants of free space, c is fixed too. This was Maxwell's proof that light is an EM wave.

What is the exact value of c from this formula?

Using µ0 = 4π×10^-7 and ε0 = 8.854×10^-12, you get c ≈ 2.998×10^8 m/s, which we round to 3×10^8 m/s in NEET numericals.

Does c change in glass or water?

The formula c = 1/√(µ0ε0) is only for vacuum. In a medium the speed is v = 1/√(µε) = c/√(µrεr), which is smaller than c. That reduction is what causes refraction.

Why is µ0ε0 equal to 1/c²?

Rearrange c = 1/√(µ0ε0). Squaring gives c² = 1/(µ0ε0), so µ0ε0 = 1/c². This identity is handy for quickly relating the two constants in problems.

Do E and B travel at different speeds in an EM wave?

No. E and B are two parts of one wave and move together at the same speed c, always in phase. Their amplitudes are related by E0 = cB0, but the speed is single and equal to c.

Related concepts:
Ratio E0/B0 = c: Relation Between Electric and Magnetic FieldsSpeed of EM Waves in a Medium v = 1/√(µε)Refractive Index from µr and εr: n = √(µr εr)Velocity of Light in a Medium Using µr and εr ProblemsKey Properties of EM Waves Travelling in Free Space
Practise Physics for NEET:
Physics MCQs (free, chapter-wise)Electromagnetic Waves PYQs