Is it correct to say: Thinking displacement current is a flow of charge across the capacitor gap?

No charge crosses the gap. i_d = ε₀ dΦ_E/dt arises from the changing electric field, and it equals the conduction current in the wires.

Is it correct to say: Taking E and B in an EM wave to be 90° out of phase?

In a travelling EM wave E and B reach their maxima and zeros together — they are in phase, though perpendicular in direction.

Is it correct to say: Calling EM waves longitudinal?

Both E and B are perpendicular to the direction of propagation, so EM waves are transverse.

Is it correct to say: Assuming frequency changes when light enters glass?

Frequency is fixed by the source. Speed and wavelength both fall by the factor n.

Is it correct to say: Writing B₀ = cE₀?

B₀ = E₀/c. The magnetic amplitude in tesla is about 3×10⁸ times smaller than E₀ in V m⁻¹.

Is it correct to say: Mixing up the order of the spectrum, e.g. putting ultraviolet at longer wavelength than infrared?

In increasing wavelength: gamma rays, X-rays, ultraviolet, visible, infrared, microwaves, radio waves.

📄 Formula sheet (PDF)

Electromagnetic Waves

Displacement current, Maxwell's equations, the nature of electromagnetic waves and the electromagnetic spectrum — NCERT Class 12 Physics Ch 8

📐 10 formulas✏️ 4 examples🎯 5 practice⚖️ Units V–VI: 18 marks (with Ch 9 and 10)🏫 CBSE📚 Class 12✓ 2025–26 syllabus

💡

Board Exam Tips

→Explain the need for displacement current with the charging capacitor: Ampère's law gives B = 0 or B ≠ 0 at the same point depending on which surface you choose, unless the displacement current between the plates is added.
→In an EM wave E, B and the direction of propagation are mutually perpendicular, and E × B points along the direction of travel.
→E₀/B₀ = c is the most-used numerical relation. Keep E in V m⁻¹ and B in tesla.
→Learn the spectrum in order of wavelength (radio, microwave, infrared, visible, ultraviolet, X-rays, gamma rays) with one source and one use for each.
→Frequency does not change when a wave enters a medium; its speed and wavelength do.

📐 Formulas(10)

Displacement Current★ Board fav

i_{d} = ε_{0} \frac{d Φ _{E}}{d t}

Symbol	Meaning
$i_{d}$	Displacement current (A)
$ε_{0}$	Permittivity of free space = 8.854×10⁻¹² C² N⁻¹ m⁻²
$Φ_{E}$	Electric flux (N m² C⁻¹)

Displacement Current in a Parallel-Plate Capacitor

i_{d} = ε_{0} A \frac{d E}{d t} = C \frac{d V}{d t}

Symbol	Meaning
$A$	Plate area (m²)
$C$	Capacitance (F)
$\frac{d V}{d t}$	Rate of change of voltage across the plates (V s⁻¹)

Ampère–Maxwell Law★ Board fav

\oint B \cdot d l = μ_{0} i_{c} + μ_{0} ε_{0} \frac{d Φ _{E}}{d t}

Symbol	Meaning
$i_{c}$	Conduction current (A)
$μ_{0}$	Permeability of free space = 4π×10⁻⁷ T m A⁻¹

Maxwell's Equations

\oint E \cdot d A = \frac{Q}{ε _{0}} \oint B \cdot d A = 0 \oint E \cdot d l = - \frac{d Φ _{B}}{d t} \oint B \cdot d l = μ_{0} i_{c} + μ_{0} ε_{0} \frac{d Φ _{E}}{d t}

Speed of EM Waves in Vacuum★ Board fav

c = \frac{1}{μ _{0} ε _{0}} \approx 3 \times 1 0^{8} m s^{- 1}

Symbol	Meaning
$c$	Speed of light in vacuum (m s⁻¹)

Speed of EM Waves in a Medium

v = \frac{1}{μ ε}

Symbol	Meaning
$v$	Speed in the medium (m s⁻¹)
$μ$	Permeability of the medium (T m A⁻¹)
$ε$	Permittivity of the medium (C² N⁻¹ m⁻²)

Plane EM Wave Travelling Along z

E_{x} = E_{0} sin (k z - ω t), B_{y} = B_{0} sin (k z - ω t)

Symbol	Meaning
$E_{0}$	Electric field amplitude (V m⁻¹)
$B_{0}$	Magnetic field amplitude (T)
$k$	Wave number (rad m⁻¹)
$ω$	Angular frequency (rad s⁻¹)

Ratio of Field Amplitudes★ Board fav

\frac{E _{0}}{B _{0}} = c

Wave Number and Angular Frequency

k = \frac{2 π}{λ}, ω = 2 π ν, ω = c k

Symbol	Meaning
$λ$	Wavelength (m)
$ν$	Frequency (Hz)

Speed, Frequency and Wavelength

c = ν λ

✏️ Solved Examples

1Solved Exampleeasy1 steps

An FM radio station broadcasts at 100 MHz. Find the wavelength of its waves and name the part of the spectrum they belong to.

Use c = νλ with c = 3×10⁸ m s⁻¹

λ = \frac{c}{ν} = \frac{3 \times 1 0 ^{8}}{100 \times 1 0 ^{6}} = 3.0 m

✅

Answer

λ = 3.0 m

2Solved Exampleboard4 steps

A plane electromagnetic wave of frequency 50 MHz travels in vacuum along the +z direction. Its electric field has amplitude 120 V m⁻¹ and points along the x-axis. Find (a) the amplitude and direction of the magnetic field, (b) ω, k and λ, and (c) expressions for E and B.

Magnetic field amplitude from E₀/B₀ = c

B_{0} = \frac{E _{0}}{c} = \frac{120}{3 \times 1 0 ^{8}} = 4.0 \times 1 0^{- 7} T

3Solved Exampleboard2 steps

A parallel-plate capacitor has plates of area 0.020 m² separated by 2.0 mm of air. The potential difference across it is increasing at 1.0×10⁶ V s⁻¹. Find the displacement current between the plates. Take ε₀ = 8.854×10⁻¹² C² N⁻¹ m⁻².

Capacitance

C = \frac{ε _{0} A}{d} = \frac{8.854 \times 1 0 ^{- 12} \times 0.020}{2.0 \times 1 0 ^{- 3}} = 8.854 \times 1 0^{- 11} F

4Solved ExampleHOTS4 steps

Light of frequency 5.0×10¹⁴ Hz passes from vacuum into a non-magnetic medium (μ_r = 1) whose relative permittivity at this frequency is 2.25. Find (a) the speed of light in the medium, (b) the refractive index and (c) the wavelength in vacuum and in the medium.

With μ = μ₀ and ε = ε_rε₀, v = 1/√(με) = c/√ε_r

v = \frac{c}{ε _{r}} = \frac{3 \times 1 0 ^{8}}{2.25} = 2.0 \times 1 0^{8} m s^{- 1}

⚠️ Traps & Common Mistakes

⚠️Common Mistakes6

1
Thinking displacement current is a flow of charge across the capacitor gap
✓No charge crosses the gap. i_d = ε₀ dΦ_E/dt arises from the changing electric field, and it equals the conduction current in the wires.
2
Taking E and B in an EM wave to be 90° out of phase
✓In a travelling EM wave E and B reach their maxima and zeros together — they are in phase, though perpendicular in direction.
3
Calling EM waves longitudinal
✓Both E and B are perpendicular to the direction of propagation, so EM waves are transverse.
4
Assuming frequency changes when light enters glass
✓Frequency is fixed by the source. Speed and wavelength both fall by the factor n.
5
Writing B₀ = cE₀
✓B₀ = E₀/c. The magnetic amplitude in tesla is about 3×10⁸ times smaller than E₀ in V m⁻¹.
6
Mixing up the order of the spectrum, e.g. putting ultraviolet at longer wavelength than infrared
✓In increasing wavelength: gamma rays, X-rays, ultraviolet, visible, infrared, microwaves, radio waves.

🎯 Practice Yourself

🎯Practice Yourself5 questions

Q1
Find the frequency of microwaves of wavelength 3.0 cm.
Q2
The magnetic field amplitude of an EM wave in vacuum is 2.0×10⁻⁸ T. Find the electric field amplitude.
Q3
Arrange in increasing order of frequency: X-rays, microwaves, visible light, infrared, gamma rays.
Q4
Name the EM waves used (a) in TV remote controls, (b) in radar and (c) to kill germs in water purifiers.
Q5
At some instant the conduction current in the wires of a charging capacitor is 2.0 A. What is the displacement current between its plates?

📝 Notes

Electromagnetic Waves

Maxwell added one term to Ampère's law and found that electric and magnetic fields can sustain each other as a wave travelling at the speed of light.

Why displacement current is needed

While a capacitor charges, a current flows in the wires but no charge crosses the gap. Ampère's law applied to a flat surface cutting the wire gives a field; applied to a pot-shaped surface passing between the plates it gives zero. The fix is the displacement current $i_d = \varepsilon_0\,d\Phi_E/dt$ , which equals the conduction current. So a changing electric field produces a magnetic field, just as a changing magnetic field produces an electric field (Faraday).

Nature of EM waves

Produced by accelerated charges; a charge oscillating at frequency $\nu$ radiates waves of frequency $\nu$ .
$\vec{E}$ , $\vec{B}$ and the direction of travel are mutually perpendicular — the waves are transverse.
$E_0/B_0 = c$ and $c = 1/\sqrt{\mu_0\varepsilon_0}$ in vacuum; $v = 1/\sqrt{\mu\varepsilon}$ in a medium.
They need no medium and carry energy from the source.

The electromagnetic spectrum

In decreasing wavelength (boundaries are approximate and overlap):

Radio waves: above 0.1 m — radio and TV broadcasting, mobile phones.
Microwaves: 0.1 m to 1 mm — radar, microwave ovens.
Infrared: 1 mm to 700 nm — remote controls, heating, night vision.
Visible light: 700 nm to 400 nm — the range the eye detects.
Ultraviolet: 400 nm to 1 nm — LASIK eye surgery, killing germs in water purifiers.
X-rays: 1 nm to about $10^{-3}$ nm — medical diagnosis.
Gamma rays: below about $10^{-3}$ nm — from nuclear reactions; used to destroy cancer cells.