Physics 30 Lesson 24: Electromagnetic Waves

Page 1: Introduction to Electromagnetic Waves

• Date and Event: On April 11, 1846, Michael Faraday was scheduled to introduce Sir Charles Wheatstone at a meeting of the Royal Society of London.

  • Wheatstone experienced severe stage fright and left before his lecture began.

  • Faraday had to deliver an unprepared lecture discussing theoretical concepts related to electromagnetic waves.

• Faraday's Background:

  • Known for well-prepared lectures and spectacular demonstrations.

  • He had made a significant discovery in 1845 regarding polarization changes in light passing through heavy glass when exposed to external magnetic fields.

  • Speculated about the connection between light and magnetism but lacked mathematical skills to advance his ideas.

  • Faraday's focus was diverted to other interests, leaving the exploration of this idea unfinished.

• James Clerk Maxwell:

  • Born (1831-1879), he began exploring Faraday's theories ten years after Faraday's initial speculation.

  • Graduated from Cambridge University in 1853 and began making significant contributions to physics and mathematics.

I. Principles of Electromagnetism

• Foundational Discoveries:

  • Oersted and Ampere discovered that:

  • A constant electric current in a conductor induces a uniform magnetic field that circles the conductor, with both fields being perpendicular.

  • A direct relationship ties electric currents and magnetic fields.

  • Henry and Faraday established the converse where:

  • A conductor moving through a perpendicular magnetic field induces a uniform current in the conductor.

• Conductors vs. Insulators:

  • Conductors: Allow the flow of electric current.

  • Insulators: Resist current flow; however, Maxwell found that a changing magnetic field momentarily shifts charges in insulators which quickly revert to their original position due to internal attractive forces.

  • This confirmed the hypothesis that changing magnetic fields can induce currents in various materials.

II. Maxwell's Extrapolations of Electromagnetism

• Induction Principles:

  • Maxwell extended Ampere's principle, stating:

  • A changing electric field in space creates a perpendicular changing magnetic field.

  • He reformulated Faraday's inductive principle, which states:

  • A changing magnetic field generates a perpendicular changing electric field.

• Interconnectedness of Fields:

  • Cycle: A changing electric field induces a changing magnetic field leading to another changing electric field, thus perpetuating the phenomenon.

III. Propagation of Electromagnetic Waves

• Creation of Waves:

  • Maxwell theorized that oscillating electric fields create electromagnetic waves.

  • Illustrated with fields:

  • An increasing electric field $E1$ induces a magnetic field $B1$, which in turn induces another electric field $E_2$, continuing indefinitely.

• Wave Characteristics:

  • Visualized as two perpendicular components:

  • Electric fields (denoted by $ε$) and magnetic fields (denoted by $β$).

  • The wave propagates perpendicularly to both fields and can travel through vacuum as it does not require a medium.

  • Electromagnetic radiation (EMR) displays transverse characteristics and can be polarized.

IV. Predictions by Maxwell

• Predictions about EM Waves:

  • Origin: Accelerating electric charge causes the formation of electromagnetic waves as it oscillates, leading to the radiation of energy in electric and magnetic fields.

  • Correspondence: The frequency of oscillation directly corresponds to the frequency of generated EM waves.

  • Speed Consistency: EM waves travel at approximately $3.00 imes 10^8 m/s$, adhering to the universal wave equation for wave mechanics represented as:

  • $c = fλ$

  • Perpendicular Properties: Electric and magnetic fields remain perpendicular to each other and the wave's propagation direction.

  • Transverse Characteristics: Interference, diffraction, refraction, and polarization are observable phenomena.

  • Observable Pressure: EM waves exert pressure when interacting with surfaces.

V. Confirmation of Maxwell's Theories by Hertz

• Hertz's Experiments:

  • In 1888, Heinrich Hertz aimed to experiment and validate Maxwell's theories regarding EM waves.

  • Hertz utilized an induction coil to create a spark and successfully detected induced sparks across a room, demonstrating the presence of EM waves.

• Findings:

  • The speed of the electromagnetic wave measured around $3.0 imes 10^8 m/s$, confirming Maxwell's prediction.

  • Hertz's observations indicated that spark generation only occurs when the receiving apparatus aligns appropriately concerning the electric and magnetic fields of the EM wave, proving polarization behavior.

  • Subsequent tests for reflection, diffraction, interference, and refraction supported the behavior of EM radiation matching that of light.

• Impact on Science:

  • Hertz's insights both confirmed Maxwell and inspired further studies, such as Marconi's work on radio transmission, establishing him as the father of radio communication.

VI. The Electromagnetic Spectrum

• Definition: EM waves exist across various frequencies classified as the electromagnetic spectrum.

• Spectrum Details:

  • The only distinction among EM waves is the frequency and wavelength.

  • Categories:

  • Low Frequency AC: ~60 Hz (used in AC power lines, creates interference).

  • Radio Waves: $10^{4} – 10^{10} Hz$ (from circuits, enables communication and navigation).

  • Microwaves: $10^{9} – 10^{12} Hz$ (applied in telecommunications and cooking).

  • Infrared Radiation: $10^{11} – 4 × 10^{14} Hz$ (relevant for thermography).

  • Visible Light: $4 × 10^{14} – 7.5 × 10^{14} Hz$ (detected by human eyes).

  • Ultraviolet Radiation: $7.5 × 10^{14} – 10^{17} Hz$ (causes tanning and fluorescence).

  • X-rays: $10^{17} – 10^{20} Hz$ (for medical imaging).

  • Gamma Rays: $10^{19} – 10^{24} Hz$ (from atomic nuclei and particle accelerators).

  • Cosmic Rays: > $10^{24} Hz$ (from cosmic phenomena).

• Memorization Aids:

  • Remember the range of visible light: 700 nm (red) to 400 nm (violet).

  • Acronym ROYGBIV for colors.

  • Categorization of frequencies:

  • Electromagnetic Types (TV, Microwave, Infrared, Visible, UV, X-rays, Gamma): $10^{8}, 10^{10}, 10^{12}, 10^{14}, 10^{16}, 10^{18}, 10^{20} Hz$ with frequency increments by a factor of 10.

• Calculation: Use the universal wave equation $c = λ f$ for wavelengths and frequencies.

VII. Assignment Questions

1. Fundamentals:

   • A. What is the fundamental origin of all EMR?

   • B. Relationship of frequency in harmonic oscillators to EMR produced.

   • C. Speed of all EMR?

   • D. Sketch an EM wave.

2. Differences Between Radiation Types:

   • Analyze similarities and differences among various radiation forms (radio, visible light, X-rays).

3. Type of Radiation by Cause:

   • Classify types of radiation based on oscillation sources and transitions of electrons.

4. Wave Penetration: X-rays or gamma rays comparison.

5. Applications of Microwaves: Cooking processes and usage in technology.

6. Camera Sensitivity: Required light type for nighttime visibility.

7. Floral Perception: Sensitivity of honey bees in light spectrum.

8. X-ray Functionality: Mechanism of using X-rays for imaging.

9. EM Signaling: Calculate travel times for radio signals over distances and analyze frequency-related phenomena.

VIII. Calculations and Responses

• Various tasks: Engage in mathematical problems resolving frequency and wavelength scenarios for EMR across various mediums.

  • E.g. Calculate the frequency of a 1.8 cm microwave. (Answer: $1.7 imes 10^{10} Hz$)

  • Determine $ ext{wavelength}$ and $ ext{periods}$ in different materials as indicated throughout the assignment tasks such as the period in Lucite or time taken for signals over astronomical distances.