Electromagnetic WavesNEET Physics · Class 12 · NCERT Chapter 8

Introduction

Light, X-rays, microwaves, gamma rays, radio waves, the Wi-Fi signal carrying this page to your phone, all are the same thing: oscillating electric and magnetic fields, travelling together at 3 × 10⁸ m/s. James Clerk Maxwell predicted them on paper in 1864, before anyone had ever generated one. Heinrich Hertz produced and detected them in his lab in 1887. This chapter is short but high-yield: NEET asks 1 question almost every year.

Common NEET asks: identifying spectrum bands (which radiation is used for sterilisation, which has highest frequency, etc.), the speed-amplitude relation E_0 = c B_0, displacement current ideas, and intensity or radiation pressure of an EM wave.

Displacement current

Ampere's circuital law in its original form was:

Maxwell noticed it failed for a charging capacitor. Pick an Amperian loop around the wire feeding one plate. If you stretch the surface bounded by the loop so it bulges between the capacitor plates, no real current passes through the surface. So the law would predict zero magnetic field, even though one is observed. The fix: add a new term, the displacement current.

Inside the capacitor, the electric flux is increasing as charge builds up; that changing flux behaves exactly like a current of equal magnitude. The corrected Ampere-Maxwell law is:

For the loop and surface trick above, I_c through the wire equals I_D between the plates, so the answer is the same whichever surface you pick.

Between the plates of a charging capacitor, no real current flows, but the changing electric flux acts as a displacement current of equal magnitude. This is what completes Ampere's law.

Maxwell's equations

With the displacement current term, the four equations describing all classical electromagnetism are:

1. Gauss for E: $\oint \vec{E}\cdot d\vec{A}=q_{\text{enc}}/{\epsilon }_0$. Source charges produce diverging E fields.
2. Gauss for B: $\oint \vec{B}\cdot d\vec{A}=0$. No magnetic monopoles.
3. Faraday: $\oint \vec{E}\cdot d\vec{l}=-d{\Phi }_B/dt$. A changing magnetic flux induces an electric field.
4. Ampere-Maxwell: $\oint \vec{B}\cdot d\vec{l}={\mu }_0(I_c+{\epsilon }_{0}d{\Phi }_E/dt)$. Currents and changing E fields produce B fields.

Read the last two together: a changing B field makes E, and a changing E field makes B. That self-sustaining loop is exactly an electromagnetic wave.

Nature of EM waves

In a plane EM wave travelling along z with E along y and B along x:

Three things to remember:

• E ⊥ B ⊥ direction of propagation. EM waves are transverse.
• E and B are in phase: they reach max together, zero together.
• $\vec{E}\times \vec{B}$ points along the direction of propagation. The Poynting vector $\vec{S}=(1/{\mu }_0)\vec{E}\times \vec{B}$ gives the rate of energy flow per area.

Only accelerating charges radiate. A static or steadily moving charge does not produce EM waves. An LC oscillator or an antenna current at frequency f radiates at the same f.

E (orange, vertical plane) and B (green, horizontal plane) oscillate in phase, perpendicular to each other and to the direction of travel (left to right).

Wave equation and amplitude relation

Maxwell's equations in free space combine into a wave equation:

The wave speed comes from the coefficients:

Comparing E and B in Maxwell's equations gives the amplitude relation:

This is one of the most-tested formulas in this chapter.

In free space the peak fields are linked by E_0 = c B_0. They oscillate in step, perpendicular to each other and to the direction the wave travels.

Speed in vacuum

Plug in ${\epsilon }_0=8.854\times 10^{-12}$ and ${\mu }_0=4\pi \times 10^{-7}$:

Same value for every EM wave: gamma rays, visible light, microwaves and radio all travel at c in vacuum.

Speed in a medium

Inside a material with relative permittivity ${\epsilon }_r$ and relative permeability ${\mu }_r$:

For most non-magnetic media (glass, water, air), ${\mu }_r\approx 1$ so n = √ε_r. Frequency does not change when the wave enters a denser medium; speed and wavelength both drop by a factor of n.

EM waves slow down in a medium: v = c / n. Frequency stays the same, wavelength shortens.

Energy and intensity

Energy density at any instant is the sum of electric and magnetic contributions:

Plug in B = E/c. With $c^2=1/({\mu }_0{\epsilon }_0)$, the two halves are equal:

Average over a full cycle (sin² average is 1/2):

Intensity is energy crossing unit area per unit time:

For a point source of power P, intensity falls off with the inverse square of distance:

Energy in an EM wave is split equally between the electric and magnetic fields. The total energy density times the speed of light equals the intensity carried.

Radiation pressure

EM waves carry momentum: $p=U/c$ for total energy U. So when a wave is absorbed by a surface, it delivers momentum and produces a pressure:

For a perfect reflector, momentum reverses, so the surface receives twice the change:

Sun delivers I ≈ 1361 W/m² at Earth, so radiation pressure is only about 4.5 × 10⁻⁶ Pa on an absorber, but enough over years to push a solar sail or shape a comet's tail.

EM waves carry momentum, so they push on surfaces. The push doubles for a perfect reflector.

The EM spectrum

Same physics, different frequencies. The full spectrum from highest to lowest frequency:

• Gamma rays(above 10¹⁹ Hz, λ < 10 pm): nuclear sources; cancer therapy, sterilisation. Highest penetration.
• X-rays (10¹⁶ to 10¹⁹ Hz, 0.01-10 nm): produced by decelerating fast electrons hitting metal; medical imaging, crystal structure (X-ray diffraction).
• Ultraviolet (10¹⁵ to 10¹⁶ Hz, 10-380 nm): Sun, mercury arcs; sterilisation, fluorescence, vitamin D in skin. Ozone layer absorbs most solar UV.
• Visible light (4 × 10¹⁴ to 7.5 × 10¹⁴ Hz, 380-750 nm): the slice your eye detects. Red has the longest wavelength, violet the shortest.
• Infrared (3 × 10¹¹ to 4 × 10¹⁴ Hz, 750 nm to 1 mm): every warm body emits IR; thermal imaging, night vision, TV remotes (around 940 nm), greenhouse effect.
• Microwaves (10⁹ to 3 × 10¹¹ Hz, 1 mm to 0.3 m): generated by klystron, magnetron, Gunn diode; microwave oven (2.45 GHz, water rotation), radar, satellite links, mobile.
• Radio waves (below 10⁹ Hz, λ ≥ 0.3 m): LC oscillators and antennas; AM (530 kHz to 1.7 MHz), FM (88-108 MHz), TV, mobile, Wi-Fi.

Click any region to see its frequency, wavelength, source and applications. The bar uses a log scale.

Convert between frequency, wavelength and photon energy. Pick which one you want to type.

Properties of EM waves to remember

• Travel at c in vacuum; same value for every band.
• Transverse: E ⊥ B ⊥ direction of propagation; can be polarised.
• E and B are in phase; $E_0=c{B}_0$.
• Carry energy and momentum: u = ε₀ E_rms², I = u c, p = U / c.
• Produced only by accelerating (or oscillating) charges.
• Do not need a medium; can travel through vacuum.
• Obey reflection, refraction, interference, diffraction and polarisation, just like visible light.

Worked NEET problems

Summary cheat sheet

• Displacement current: $I_D={\epsilon }_{0}d{\Phi }_E/dt$.
• Speed in vacuum: $c=1/\sqrt{{\mu }_0{\epsilon }_0}$.
• Speed in medium: $v=c/n,n=\sqrt{{\mu }_r{\epsilon }_r}$.
• Amplitude: $E_0=c{B}_0$.
• Energy density: $u={\epsilon }_0{E}_{\text{rms}}^2$, split equally between E and B.
• Intensity: $I=uc=\frac{1}{2}{\epsilon }_{0}c{E}_0^2$.
• Point source: $I=P/(4\pi r^2)$.
• Pressure (absorber): $P=I/c$. (Reflector): $P=2I/c$.
• Spectrum order (high f → low f): γ → X → UV → visible → IR → microwave → radio.

Next: try the interactive widgets for displacement current, EM spectrum and radiation pressure, or work through the 30 NEET PYQs with full solutions. To time yourself, take the free 10-question mock test.