Electromagnetic Waves: CBSE Class 12 Physics Chapter 8 Notes

Key Terminology

Displacement Current (I_d)

A current that comes into existence, in addition to the conduction current, whenever the electric field and hence the electric flux changes with time. Formula: I_d = ε₀ (dΦ_E/dt).

Electromagnetic (EM) Waves

Waves produced by accelerated charges, consisting of oscillating electric and magnetic fields that are perpendicular to each other and to the direction of wave propagation.

Electromagnetic Spectrum

The classification of electromagnetic waves according to their frequency or wavelength. It spans from radio waves (lowest frequency) to gamma rays (highest frequency).

Poynting Vector (S)

A vector representing the directional energy flux (the energy transfer per unit area per unit time) of an electromagnetic field. S = (1/μ₀) (E x B).

Wavelength (λ)

The spatial period of a periodic wave; the distance over which the wave's shape repeats. Measured in meters.

Frequency (ν or f)

The number of occurrences of a repeating event per unit of time. For EM waves, it's the number of oscillations per second. Measured in Hertz (Hz).

Ampere-Maxwell Law

The modified form of Ampere's circuital law which includes displacement current. ∮ B ⋅ dl = μ₀(I_c + I_d) = μ₀(I_c + ε₀ dΦ_E/dt).

Displacement Current & Maxwell's Correction

Before Maxwell, Ampere's Circuital Law (∮ B ⋅ dl = μ₀I) was thought to be complete. However, it had a major inconsistency. Consider the process of charging a capacitor. If we apply Ampere's law to a loop placed around the connecting wire, the enclosed current (conduction current, I_c) is non-zero, so there is a magnetic field. But if we consider a surface that passes between the capacitor plates (like a tiffin box with one side between the plates), the conduction current is zero, yet a magnetic field is still observed. This contradiction showed that Ampere's law was incomplete. James Clerk Maxwell resolved this by proposing the existence of a displacement current (I_d). He argued that a changing electric field between the capacitor plates is equivalent to a current. This displacement current is given by I_d = ε₀ (dΦ_E/dt), where Φ_E is the electric flux. This current is not a flow of charges but a consequence of the time-varying electric field. By adding this term, Ampere's law becomes the Ampere-Maxwell Law, which is universally valid. This was the final piece of the puzzle that led to the prediction of electromagnetic waves.

Properties of Electromagnetic Waves

• EM waves are produced by accelerated charges and do not require a material medium for propagation (they can travel in a vacuum).
• They are transverse in nature. The oscillating electric field (E), magnetic field (B), and the direction of propagation (k) are mutually perpendicular.
• The electric and magnetic fields oscillate in the same phase.
• In a vacuum, all EM waves travel at the speed of light, c ≈ 3 x 10⁸ m/s. The speed is given by c = 1/√(μ₀ε₀).
• In a medium, the speed is v = 1/√(με), where μ and ε are the permeability and permittivity of the medium.
• The ratio of the magnitudes of the electric and magnetic fields is constant: E/B = c (in vacuum) or E/B = v (in a medium).
• EM waves carry energy and momentum. The energy is shared equally between the electric and magnetic fields. Energy density u = u_E + u_B = (1/2)ε₀E² + (1/2μ₀)B².
• They exert radiation pressure when they strike a surface. Momentum transferred is p = U/c (for complete absorption) or p = 2U/c (for complete reflection), where U is the energy.
• EM waves are not deflected by electric or magnetic fields as they are uncharged.

The Electromagnetic Spectrum at a Glance

Maxwell's Equations (Integral Form)

Quick Worked Examples

• {"name":"Calculating B from E","problem":"The electric field of a plane EM wave in a vacuum is given by E = 3.0 x 10⁻⁵ sin(kx - ωt) ĵ N/C. Find the amplitude of the magnetic field.","solution":"We know the relationship between the amplitudes of the electric (E₀) and magnetic (B₀) fields is E₀ / B₀ = c. \nGiven E₀ = 3.0 x 10⁻⁵ N/C and c = 3 x 10⁸ m/s.\nB₀ = E₀ / c = (3.0 x 10⁻⁵ N/C) / (3 x 10⁸ m/s) = 1.0 x 10⁻¹³ T.\nThe amplitude of the magnetic field is 1.0 x 10⁻¹³ Tesla."}
• {"name":"Calculating Wavelength from Frequency","problem":"A radio station broadcasts at a frequency of 100 MHz. What is the wavelength of the EM waves broadcasted?","solution":"The relationship between speed (c), frequency (ν), and wavelength (λ) is c = νλ.\nGiven ν = 100 MHz = 100 x 10⁶ Hz = 1 x 10⁸ Hz.\nλ = c / ν = (3 x 10⁸ m/s) / (1 x 10⁸ Hz) = 3 meters."}

Exam Traps & Scoring Tips

Board Exam Hotspots:

1. Spectrum Order & Uses: A very common 1-2 mark question asks you to arrange a few EM waves in order of increasing/decreasing wavelength or frequency. You will almost certainly be asked for one use of Infrared, UV, X-rays, or Microwaves. Memorize the spectrum table!
2. Displacement Current: Be ready to explain why displacement current was needed (inconsistency of Ampere's law for a charging capacitor). The derivation is not usually asked, but the concept is key.
3. Properties of EM Waves: Questions asking for 2 or 4 properties are frequent. Remember to mention the transverse nature, the relation E/B = c, and that they don't require a medium.
4. Direction of Propagation: If given E in ĵ direction and B in k̂ direction, the direction of propagation is given by the cross product E x B, which is î direction (i.e., along the x-axis).

Quick Revision Check

• What is the fundamental source of electromagnetic waves? An accelerated electric charge.
• Arrange the following in increasing order of wavelength: Gamma rays, Microwaves, UV rays. Gamma rays < UV rays < Microwaves.
• An EM wave is travelling in the z-direction. The electric field is along the x-axis. What is the direction of the magnetic field? The magnetic field must be along the y-axis. The three (E, B, and direction of propagation) must be mutually perpendicular, and the direction of propagation is given by E x B.
• Why are X-rays used for medical imaging but not radio waves? X-rays have very short wavelengths and high energy, allowing them to penetrate soft tissues but be absorbed by denser materials like bones, creating a shadow image. Radio waves have very long wavelengths and low energy, so they pass through the body without interaction.

Frequently Asked Questions