The trap that costs marks here is a units trap, not a physics one. An EM wave question hands you E₀ in V/m and asks for B₀ in tesla — or the reverse — and the amplitude gets copied across with the wrong unit attached, or the factor c gets dropped entirely. E and B in an electromagnetic wave are not numerically comparable in SI. They differ by roughly 3 × 10⁸, and they carry different dimensions: V/m against T, which is kg/(A·s²).
The relation is one line: E₀ = c B₀, equivalently E₀/B₀ = c. NCERT Class 12 Physics Chapter 8 states this alongside the wave's field structure on printed page 206. Read it in the direction the question needs: given E₀, divide by c to get B₀ in tesla; given B₀, multiply by c to get E₀ in V/m. Because c ≈ 3 × 10⁸ m/s, the magnetic amplitude in an ordinary laboratory wave is a very small number — microtesla or smaller — while the electric amplitude sits in the hundreds of V/m. If your answer has B₀ of the same order as E₀, you have skipped the conversion.
Two more facts from the same chapter carry their own questions. The wave's speed in vacuum follows from Maxwell's equations as c = 1/√(μ₀ε₀), given on printed page 204 — a speed built entirely from two electric and magnetic constants of free space, with no mechanical medium anywhere in it. And the average intensity of a plane wave, I = ½ c ε₀ E₀², is quadratic in the electric amplitude: double E₀ and the intensity goes up four times, not two.
Watch-out for the exam: whenever an option list mixes V/m and T values, check the unit on the quantity you were asked for before you check the arithmetic. The distractor is usually the correct number with the wrong unit, or the given amplitude returned unchanged.
Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.
In a plane electromagnetic wave travelling in vacuum, the peak electric field E₀ and peak magnetic field B₀ are related by
Answer: C. C is correct. The amplitude relation for a plane EM wave in vacuum is E₀ = c B₀, stated in NCERT Class 12 Physics Chapter 8 on printed page 206.
Why A is wrong: A is wrong because it equates the two amplitudes numerically. E and B are not interchangeable in SI — they carry different dimensions (V/m versus T) and differ by a factor of about 3 × 10⁸.
Why B is wrong: B is wrong because it inverts the relation. Dividing E₀ by c would give a value of the order of B₀, so this form would make the electric amplitude the smaller of the two — the opposite of what the wave shows.
Why D is wrong: D is wrong because it introduces a spurious second factor of c. Only one power of c appears in the amplitude relation; c² appears in 1/(μ₀ε₀), which is a different result.
A plane electromagnetic wave in vacuum has a peak magnetic field of 2.0 × 10⁻⁸ T. Taking c = 3.0 × 10⁸ m/s, the peak electric field is
Answer: B. B is correct. E₀ = c B₀ = (3.0 × 10⁸)(2.0 × 10⁻⁸) = 6.0 V/m, using the amplitude relation from NCERT Class 12 Physics Chapter 8, printed page 206.
Why A is wrong: A is wrong because it returns the given magnetic amplitude unchanged with the electric unit attached. This is the unit-confusion trap: the conversion factor c has been dropped entirely.
Why C is wrong: C is wrong because it divides by c instead of multiplying. Going from B₀ to E₀ requires multiplication by c; division is the reverse direction.
Why D is wrong: D is wrong because it multiplies by c twice (c² B₀). Only one factor of c relates the two amplitudes.
The peak electric field of a plane electromagnetic wave in vacuum is 9.0 × 10² V/m. Taking c = 3.0 × 10⁸ m/s, the peak magnetic field is
Answer: A. A is correct. B₀ = E₀ / c = (9.0 × 10²) / (3.0 × 10⁸) = 3.0 × 10⁻⁶ T, from the relation given in NCERT Class 12 Physics Chapter 8, printed page 206.
Why B is wrong: B is wrong because it multiplies by c when the question requires division. Multiplying is the B₀ → E₀ direction, not E₀ → B₀.
Why C is wrong: C is wrong because it copies the given electric amplitude across and relabels it as tesla. The number is unconverted and the unit does not belong to it — the amplitude-versus-unit confusion in its plainest form.
Why D is wrong: D is wrong because the arithmetic is correct but the unit is not. The question asks for a magnetic field, which is measured in tesla, not V/m; these are different SI dimensions.
The SI units of the peak electric field and the peak magnetic field of an electromagnetic wave are, respectively,
Answer: C. C is correct. The electric field is measured in volt per metre and the magnetic field in tesla; tesla expands to kg/(A·s²), a different dimension from V/m. NCERT Class 12 Physics Chapter 8 uses these units throughout the wave discussion, printed page 206.
Why A is wrong: A is wrong because it swaps the two units — exactly the reversal that produces a magnetic field quoted in V/m and an electric field in tesla.
Why B is wrong: B is wrong because it gives both fields the electric unit. That would make E and B dimensionally identical, which they are not in SI.
Why D is wrong: D is wrong because it gives both fields the magnetic unit, the mirror of option B and equally dimensionally inconsistent.
According to Maxwell's equations, the speed of electromagnetic waves in vacuum is given by
Answer: D. D is correct. Maxwell's equations give c = 1/√(μ₀ε₀) ≈ 3 × 10⁸ m/s, stated in NCERT Class 12 Physics Chapter 8 on printed page 207.
Why A is wrong: A is wrong because it takes the product rather than the reciprocal of its square root. μ₀ε₀ is numerically about 1.1 × 10⁻¹⁷ in SI, nowhere near a speed.
Why B is wrong: B is wrong because it omits the reciprocal. √(μ₀ε₀) equals 1/c, so this expression gives the reciprocal of the speed.
Why C is wrong: C is wrong because it omits the square root. 1/(μ₀ε₀) equals c², which has units of m²/s² and is not a speed.
The average intensity of a plane electromagnetic wave is I = ½ c ε₀ E₀². If the peak electric field of the wave is doubled while the wave still travels in vacuum, the average intensity becomes
Answer: C. C is correct. Intensity depends on the square of the peak electric field, so doubling E₀ multiplies I by 2² = 4. The intensity expression appears in NCERT Class 12 Physics Chapter 8, printed page 206.
Why A is wrong: A is wrong because it treats the dependence as inverse. Intensity increases with electric amplitude; it does not fall when the amplitude rises.
Why B is wrong: B is wrong because it treats the dependence as linear. The E₀ in the formula is squared, so the factor is 4 and not 2.
Why D is wrong: D is wrong because it treats intensity as independent of amplitude. Only c and ε₀ are constants in the expression; E₀ is the variable the question changes.
A plane electromagnetic wave in vacuum has a peak magnetic field of 1.0 × 10⁻⁷ T. Taking c = 3.0 × 10⁸ m/s and ε₀ = 8.85 × 10⁻¹² F/m, the average intensity of the wave is closest to
Answer: B. B is correct. First E₀ = c B₀ = (3.0 × 10⁸)(1.0 × 10⁻⁷) = 30 V/m; then I = ½ c ε₀ E₀² = ½ (3.0 × 10⁸)(8.85 × 10⁻¹²)(30)² ≈ 1.2 W/m². Both relations are from NCERT Class 12 Physics Chapter 8, printed page 206.
Why A is wrong: A is wrong because it drops the factor ½: c ε₀ E₀² = 2.4 W/m² is the peak, not the average, intensity.
Why C is wrong: C is wrong because it forgets to square the amplitude: ½ c ε₀ E₀ = 4.0 × 10⁻², which is not even an intensity dimensionally.
Why D is wrong: D is wrong because ½ε₀E₀² ≈ 4.0 × 10⁻⁹ J/m³ is the average energy density; intensity needs the extra factor c, the speed at which that energy is carried.
A student computing the magnetic amplitude of a laboratory electromagnetic wave with peak electric field of a few hundred V/m obtains an answer of the same order of magnitude as the electric amplitude. The most likely explanation is that the student has
Answer: D. D is correct. Since E₀ = c B₀ with c ≈ 3 × 10⁸ m/s, a magnetic amplitude of the same order as the electric one can only arise if the division by c was never performed. NCERT Class 12 Physics Chapter 8 gives the relation on printed page 206.
Why A is wrong: A is wrong because a unit error alone would not change the magnitude. Relabelling a correctly computed 10⁻⁶-order number as V/m still leaves it far smaller than the electric amplitude.
Why B is wrong: B is wrong because neither frequency nor wavelength enters the amplitude relation. E₀ = c B₀ holds at every frequency in the spectrum.
Why C is wrong: C is wrong because a change of medium alters the wave speed only modestly, by a factor of the refractive index. It cannot close a gap of 10⁸ between the two amplitudes.
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Pattern: P.PHY.U15.EM_WAVE_E_B_RATIO — EM wave amplitude relation, E₀ = c B₀ (frequency 3; years observed 2020, 2024, 2025).
Given
A plane electromagnetic wave travels in vacuum with a peak magnetic field B₀ = 4.0 × 10⁻⁸ T.
Speed of light in vacuum c = 3.0 × 10⁸ m/s.
Required
The peak electric field E₀ of the wave, in V/m.
Concept
In a plane electromagnetic wave the electric and magnetic fields oscillate in phase, perpendicular to each other and to the direction of propagation, and their amplitudes are locked together by the wave speed. They are not independent quantities and they are not numerically comparable — the electric amplitude is larger by a factor of c.
Formula
E₀ / B₀ = c, so E₀ = c B₀.
(NCERT Class 12 Physics Chapter 8, printed page 206.)
Substitution
E₀ = (3.0 × 10⁸ m/s) × (4.0 × 10⁻⁸ T)
Calculation
Coefficients: 3.0 × 4.0 = 12
Powers of ten: 10⁸ × 10⁻⁸ = 10⁰ = 1
E₀ = 12 V/m = 1.2 × 10¹ V/m
Both given values carry two significant figures, and c is supplied here as a problem-defined value to two significant figures rather than as an exact constant, so the answer is quoted to two significant figures.
Final answer
E₀ = 1.2 × 10¹ V/m
Written as 12 V/m the trailing zero is not ambiguous here, but the scientific form makes the two-significant-figure claim explicit.
Common trap
The distractor to expect is 4.0 × 10⁻⁸ V/m — the given number returned unchanged with the electric unit stuck on it. It appears whenever the conversion factor c is dropped. The second-most common is division instead of multiplication, giving 1.3 × 10⁻¹⁶ V/m. Check the direction before you compute: going from tesla to volt per metre you multiply by c, because the electric amplitude is the larger one. A magnetic amplitude in the microtesla range paired with an electric amplitude in the hundreds of V/m is the shape a correct answer has.
Similar NEET-style question
A plane electromagnetic wave in vacuum has a peak electric field of 1.5 × 10² V/m. Taking c = 3.0 × 10⁸ m/s, find the peak magnetic field and state its unit.
*(Answer: B₀ = E₀/c = 5.0 × 10⁻⁷ T.)*
Self-sustaining oscillating E and B fields propagating through space. Speed in vacuum: c = 1/√(μ₀ε₀) ≈ 3 × 10⁸ m/s. E and B mutually perpendicular and both perpendicular to propagation direction (transverse).
-- NCERT Class 12 Physics, Ch. 8, p. 207E_0/B_0 = c. Energy density: u = (1/2) ε₀ E² + B²/(2μ₀). Equal contributions from E and B fields. Intensity: I = u·c = (1/2) c ε₀ E_0².
-- NCERT Class 12 Physics, Ch. 8, p. 207Average power per unit area carried by EM wave with peak field E0.
| Symbol | Quantity | SI Unit |
|---|---|---|
| I | intensity | W/m^2 |
| E0 | peak field | V/m |
| c | speed | m/s |
| eps0 | permittivity | F/m |
In an EM plane wave, the amplitudes of E and B are related by speed of light.
| Symbol | Quantity | SI Unit |
|---|---|---|
| E0 | E peak | V/m |
| B0 | B peak | T |
Speed of EM waves in vacuum from Maxwell's equations. ~3e8 m/s.
| Symbol | Quantity | SI Unit |
|---|---|---|
| c | speed in vacuum | m/s |
| mu0 | permeability | T*m/A |
| eps0 | permittivity | F/m |
These are the exact patterns that cause wrong answers in NEET. Each trap includes when it triggers and how to avoid it.
Category: Unit Conversion
Student reports E in T or B in V/m, conflating the two amplitudes. They differ by factor c; same SI dimensions in Gaussian units only.
EM wave question gives E0 (V/m) and asks for B0 (T) or vice versa.
Always: E (V/m) = c × B (T). c ≈ 3×10⁸ converts. E and B have different SI dimensions.
Root cause: unit error
E (V/m) = c × B (T). The amplitudes differ by factor c≈3×10⁸. They have different SI dimensions (V/m vs T = kg/(A·s²)).
More in Electromagnetic Waves: 1 formula · 2 question patterns from its other lessons.
The property which is not of an electromagnetic wave travelling in free space is that:
forgets c conversion
Equates E and B without c factor
Page numbers are the ones printed in the current NCERT textbook (2023 rationalised edition), unless marked pre-2023. The books are free at ncert.nic.in.
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