Electromagnetic Waves

Electromagnetic Waves explains how changing electric and magnetic fields sustain each other and travel through space, carrying energy from the Sun to the Earth and signals from mobile towers to our phones. In this chapter you will learn how Maxwell found an inconsistency in Ampere's circuital law when applied to a charging capacitor, and removed it by introducing the displacement current, epsilon0 times the rate of change of electric flux. This led to the prediction of electromagnetic waves travelling at speed c = 1/sqrt(mu0 epsilon0), which matched the measured speed of light. You will study how electromagnetic waves are produced by accelerating charges, and their nature: they are transverse, the electric and magnetic fields oscillate in phase and perpendicular to each other and to the direction of travel, and E0/B0 = c. Hertz confirmed them experimentally. The chapter describes the electromagnetic spectrum from radio waves, microwaves, infrared, visible light and ultraviolet to X-rays and gamma rays, with their frequency ranges, sources and everyday uses.

Detailed Worksheet: Electromagnetic Waves Section A - Definitions (10 marks) 1. What is displacement current? Write its expression. (2 marks) 2. Write the Ampere-Maxwell law and explain the significance of the extra term. (2 marks) 3. State two characteristics of electromagnetic waves. (2 marks) 4. What is the source of electromagnetic waves? Can a charge moving with uniform velocity produce them? (2 marks) 5. Name the electromagnetic waves used for (i) radar and (ii) killing germs in water purifiers. (2 marks) Section B - Calculations and Applications (15 marks) 6. A parallel plate capacitor with circular plates of radius 12 cm and separation 5 mm is charged by a current of 0.15 A. Find the displacement current between the plates and the rate of change of the electric field (epsilon0 = 8.85 x 10^-12 C^2 N^-1 m^-2). (3 marks) 7. The amplitude of the magnetic field of a plane electromagnetic wave in vacuum is 510 nT. Find the amplitude of the electric field. (3 marks) 8. An FM radio station broadcasts at 100 MHz. Find the wavelength of its waves. In which part of the spectrum do they lie? (3 marks) 9. Light of wavelength 500 nm travels in vacuum. Find its frequency. To which colour does it correspond? (3 marks) 10. Using mu0 = 4 pi x 10^-7 T m/A and epsilon0 = 8.854 x 10^-12 C^2 N^-1 m^-2, calculate the speed of electromagnetic waves in vacuum. (3 marks) Section C - Diagrams (10 marks) 11. Draw a diagram of a plane electromagnetic wave travelling along the z-direction, showing the oscillating electric field along x and magnetic field along y. (4 marks) 12. Draw a diagram of a charging capacitor with two surfaces bounded by the same loop, one cut by the wire and one passing between the plates, to show why displacement current is needed. (3 marks) 13. Draw a chart of the electromagnetic spectrum in order of increasing frequency, writing approximate wavelength ranges for each band. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. Explain the inconsistency in Ampere's circuital law in the case of a charging capacitor and how Maxwell resolved it. Show that the displacement current between the plates equals the conduction current in the wires. (5 marks) 15. Describe the electromagnetic spectrum, giving for each band its frequency range, a method of production or detection, and one use. (5 marks) 16. The electric field of a plane electromagnetic wave is Ey = 60 sin(0.5 x 10^3 x + 1.5 x 10^11 t) V/m. Find (i) the wavelength, (ii) the frequency, (iii) the amplitude of the magnetic field and (iv) the direction of propagation and of the magnetic field. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Use c = 3 x 10^8 m/s and show units. Draw neat, labelled diagrams.