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Foundation8 past questions

Mathematical relations in electromagnetic waves

Key mathematical relationships in electromagnetic waves include the connection between electric and magnetic field amplitudes, wave speed, wavelength, frequency, and the wave equation parameters.

Why this shows up in the exam

NEET frequently tests your ability to use and manipulate these equations to solve problems involving electromagnetic waves.

How NEET tests this

Numerical · 5 QsDirect recall · 3 QsApplication

Learn the idea

When an EM wave passes from one medium to another its frequency stays fixed; the change in speed (v = c/n) forces the wavelength to adjust as λ = v/f.

🧠 Memory hook: Higher n means slower light, so the wave’s ‘stretch’ (λ) shrinks while its beat (f) stays the same.

Get this one clearly and it pays off every single time it shows up in the paper. 🎯

Formulas & facts to keep ready

  • v = c/n where n = √(ε_r μ_r) (NCERT Eq. 2.1)
  • For non‑magnetic media μ_r = 1, so n = √ε_r
  • Frequency f is determined by the source and does not change at an interface
  • λ = v/f links wavelength, speed and frequency
  • Relative permittivity ε_r = ε/ε₀ (ε₀ = 8.85×10⁻¹² F m⁻¹)
  • c = 3×10⁸ m s⁻¹ in vacuum

How to approach it

  1. 1Read the given quantities – note the frequency and the relative permittivity (or ε) of the new medium
  2. 2Compute the refractive index n = √ε_r (μ_r =1 for most NEET problems)
  3. 3Find the new speed v = c/n
  4. 4Use λ = v/f; keep f unchanged to obtain the new wavelength
  5. 5State the change qualitatively if asked (e.g., λ becomes 1/n of its original)

Worked example — watch it click

An electromagnetic wave of frequency 4 MHz enters from vacuum into a medium having permittivity, ε = 9. Then its

  • A)Wavelength triples and the frequency remains con-stant
  • B)Wavelength triples and frequency becomes one third
  • ✅Wavelength becomes one third and frequency remains unchanged
  • D)Wavelength and frequency remain unchanged

The concept behind this problem

The problem checks whether you remember that only speed and wavelength are altered by the medium’s refractive index, not the frequency.

Step by step

  1. 1When EM wave enters a medium: v = c/n where n = √(εᵣμᵣ).
  2. 2For non-magnetic medium μᵣ=1, so n = √ε = √9 = 3.
  3. 3Speed becomes v = c/3.
  4. 4Frequency remains constant (determined by source).
  5. 5Since v = fλ, and v becomes 1/3 while f is constant, wavelength λ becomes 1/3.

Watch out

Many students incorrectly let the wavelength increase, forgetting that λ varies inversely with the refractive index.

Common slip-ups that cost marks

  • •Treating the given ε as absolute instead of relative and forgetting to divide by ε₀
  • •Assuming the frequency changes inside the medium
  • •Mixing up the direction of change: higher n → lower speed → shorter wavelength

🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.

Practise it

These are real questions from past NEET papers that test this exact idea.

Question 1 of 8

An electromagnetic wave of frequency 4 MHz enters from vacuum into a medium having permittivity, ε = 9. Then its

Push further

More challenging

6 harder questions built from the past papers above — a step up in difficulty, with distractors designed so you can't get there by elimination. Written and checked by our reviewers, not from a real paper.

Question 1 of 6

A capacitor is connected to an AC voltage source V = V₀ cos(ωt). Which of the following correctly represents the displacement current (I_d) between its plates?

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