PhysicsClass 12Electromagnetic Waves

Electromagnetic Waves | Class 12 Physics Notes

By ConceptScroll Team · Published on 17 July 2026 · 5 min read

Electromagnetic Waves | Class 12 Physics Notes

Electromagnetic Waves – this guide gives you a concise, exam-ready overview of Electromagnetic Waves from Class 12 Physics, written by ConceptScroll editors and reviewed against the latest NCERT textbook.

8.1 INTRODUCTION

In earlier chapters, we learned that an electric current produces a magnetic field and that two current-carrying wires exert forces on each other due to their magnetic fields. Additionally, a changing magnetic field produces an electric field, as seen in Faraday's law of electromagnetic induction. The question arises: does a changing electric field also produce a magnetic field? James Clerk Maxwell answered this affirmatively, proposing that not only electric currents but also time-varying electric fields generate magnetic fields. While applying Ampere's circuital law to a charging capacitor, Maxwell noticed an inconsistency. The law, as originally formulated, did not account for the magnetic field in the region between the capacitor plates where no conduction current flows. To resolve this, Maxwell introduced the concept of displacement current, an additional current term arising from the changing electric field. This addition made Ampere's law consistent and symmetric with Faraday's law.

Maxwell formulated a set of four equations, now known as Maxwell's equations, that unify electricity, magnetism, and optics. These equations describe how electric and magnetic fields are generated by charges, currents, and changes in each other. One of the most profound predictions from Maxwell's equations is the existence of electromagnetic waves—coupled oscillations of electric and magnetic fields that propagate through space at a speed very close to the speed of light (3 × 10^8 m/s). This led to the remarkable conclusion that light itself is an electromagnetic wave, unifying the previously separate domains of electricity, magnetism, and optics. Heinrich Hertz experimentally demonstrated electromagnetic waves in 1885, confirming Maxwell's prediction. Subsequently, the technological exploitation of these waves revolutionized communication.

This chapter begins by discussing the need for displacement current and its implications, followed by a qualitative description of electromagnetic waves and their properties. Finally, the chapter covers the electromagnetic spectrum, spanning from gamma rays with extremely short wavelengths to long radio waves with very large wavelengths.

📊 Diagram: See figure_1: James Clerk Maxwell (1831 - 1879) Born in Edinburgh, Scotland, was among the greatest physicists of the nineteenth century. He derived the thermal velocity distribution of molecules in a gas and was among the first to obtain reliable estimates of molecular parameters from measurable quantities like viscosity, etc. Maxwell's greatest achievement was the unification of the laws of electricity and magnetism (discovered by Coulomb, Oersted, Ampere and Faraday) into a consistent set of equations now called Maxwell's equations. From these he arrived at the most important conclusion that light is an electromagnetic wave. Interestingly, Maxwell did not agree with the idea (strongly suggested by the Faraday's laws of electrolysis) that electricity was particulate in nature.

🔗 Connection: This introduction sets the stage for the next section on displacement current, explaining why Maxwell introduced this concept to resolve inconsistencies in Ampere's law.

Frequently asked questions

8.1 Figure 8.5 shows a capacitor made of two circular plates each of radius 12 cm, and separated by 5.0 cm. The capacitor is being charged by an external source (not shown in the figure). The charging current is constant and equal to 0.15 A. (a) Calculate the capacitance and the rate of change of potential difference between the plates. (b) Obtain the displacement current across the plates. (c) Is Kirchhoff's first rule (junction rule) valid at each plate of the capacitor? Explain.

Given: Radius of plates, r = 12 cm = 0.12 m Separation between plates, d = 5.0 cm = 0.05 m Charging current, I = 0.15 A

(a) Calculate capacitance C: Capacitance of parallel plate capacitor, C = ε₀ A / d Area, A = π r² = π × (0.12)² = π × 0.0144 = 0.04524 m² ε₀ = 8.854 × 10⁻¹² F/m So, C = (8.854 × 10⁻¹²) × 0.04524 / 0.05 = 8.01 × 10⁻¹² F = 8.01 pF

Rate of change of potential difference (dV/dt): Current I = C (dV/dt) ⇒ dV/dt = I / C = 0.15 / (8.01 × 10⁻¹²) = 1.87 × 10¹⁰ V/s

(b) Displacement cur

8.2 A parallel plate capacitor (Fig. 8.6) made of circular plates each of radius R = 6.0 cm has a capacitance C = 100 pF. The capacitor is connected to a 230 V ac supply with a (angular) frequency of 300 rad s⁻¹. (a) What is the rms value of the conduction current? (b) Is the conduction current equal to the displacement current? (c) Determine the amplitude of B at a point 3.0 cm from the axis between the plates.

Given: Radius R = 6.0 cm = 0.06 m Capacitance C = 100 pF = 100 × 10⁻¹² F Voltage amplitude V₀ = 230 V (rms given, so V_rms = 230 V) Angular frequency ω = 300 rad/s

(a) RMS conduction current I_rms: For capacitor, current leads voltage by 90° I = C dV/dt = C ω V₀ cos(ω t) RMS current I_rms = ω C V_rms I_rms = 300 × 100 × 10⁻¹² × 230 = 6.9 × 10⁻⁶ A = 6.9 μA

(b) The conduction current in the wires is equal in magnitude to the displacement current between the plates because the displacement curren

8.3 What physical quantity is the same for X-rays of wavelength 10⁻¹⁰ m, red light of wavelength 6800 Å and radiowaves of wavelength 500 m?

The physical quantity that is the same for all electromagnetic waves, regardless of their wavelength, is the speed of the wave in vacuum. All electromagnetic waves travel at the speed of light, c = 3 × 10⁸ m/s.

8.4 A plane electromagnetic wave travels in vacuum along z-direction. What can you say about the directions of its electric and magnetic field vectors? If the frequency of the wave is 30 MHz, what is its wavelength?

In a plane electromagnetic wave traveling along the z-direction, the electric field vector (E) and magnetic field vector (B) are perpendicular to each other and both are perpendicular to the direction of propagation (z-axis). Thus, E and B lie in the x-y plane.

Frequency, ν = 30 MHz = 30 × 10⁶ Hz Wavelength, λ = c / ν = (3 × 10⁸ m/s) / (30 × 10⁶ Hz) = 10 m

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