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Chapter Analysis
Advanced13 pages • EnglishQuick Summary
The chapter on electromagnetic waves begins by discussing the need for the displacement current, a concept introduced by Maxwell to address inconsistencies in Ampere's circuital law. This leads to the unified view of electricity, magnetism, and light, establishing electromagnetic waves as coupled time-varying electric and magnetic fields that propagate in space. Various types of electromagnetic waves are explored, including their properties, propagation, and roles in technology and nature.
Key Topics
- •Displacement current
- •Maxwell's equations
- •Electromagnetic spectrum
- •Propagation of electromagnetic waves
- •Sources of electromagnetic waves
- •Nature of electromagnetic waves
- •Technological applications of electromagnetic waves
- •Electromagnetic wave interactions with matter
Learning Objectives
- ✓Understand the role of displacement current in electromagnetic theory.
- ✓Describe how electromagnetic waves are generated and propagate.
- ✓Identify different types of electromagnetic waves and their properties.
- ✓Explain the significance of Maxwell's equations in understanding electromagnetism.
- ✓Apply knowledge of the electromagnetic spectrum to practical applications.
- ✓Analyze the interaction of electromagnetic waves with different materials.
Questions in Chapter
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 0.15A. (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.
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A parallel plate capacitor 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 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.
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What physical quantity is the same for X-rays of wavelength 10–10 m, red light of wavelength 6800 Å and radiowaves of wavelength 500m?
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A plane electromagnetic wave travels in vacuum along the 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?
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A radio can tune into any station in the 7.5 MHz to 12 MHz band. What is the corresponding wavelength band?
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Additional Practice Questions
Explain the role of James Clerk Maxwell in the development of electromagnetic theory.
mediumAnswer: James Clerk Maxwell developed a set of equations that unified electricity, magnetism, and light into a coherent theory. His equations predicted the existence of electromagnetic waves which travel at the speed of light, thus confirming the idea that light is an electromagnetic wave. His work laid the foundational framework for modern electromagnetic theory.
Discuss how electromagnetic waves are propagated in a vacuum.
mediumAnswer: In a vacuum, electromagnetic waves propagate as self-sustaining oscillations of electric and magnetic fields at right angles to each other and to the direction of wave propagation. This propagation occurs without the need for a physical medium, as the fields regenerate each other through continuous oscillation.
Describe the significance of the electromagnetic spectrum and its various components.
hardAnswer: The electromagnetic spectrum encompasses all types of electromagnetic radiation, ranging from gamma rays with very short wavelengths to radio waves with very long wavelengths. Each type of radiation has its own specific uses, from medical imaging with X-rays to communication with radio waves. The variety in electromagnetic spectrum allows for diverse technological applications and natural phenomena explanations.
Explain how oscillating charges produce electromagnetic waves.
mediumAnswer: Oscillating charges induce changes in their electric fields, which cause changes in magnetic fields, leading to the continual regeneration of both fields. This interaction propagates through space as electromagnetic waves, with the frequency of the wave equal to the oscillation frequency of the charge.
How do the properties of electromagnetic waves differ in various mediums?
hardAnswer: In different mediums, electromagnetic waves experience changes in speed based on the medium's permittivity and permeability. The refractive index of the medium affects how electromagnetic waves bend. These properties influence wave behaviors like reflection, refraction, and dispersion.