Energy Systems Course Quiz
45 Questions
2 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

Who is the Ussher Assistant Professor for the Science of Energy and Energy Systems for this course?

  • David McCloskey (correct)
  • Addison Wesley
  • George B. Thomas
  • H.M. Schey
  • Which of the following is NOT a primary focus of this course?

  • Providing mathematical tools to describe light as a wave in a vector field.
  • Analyzing chemical reactions in energy systems (correct)
  • Connecting Electricity, Magnetism, and Light
  • Exploring the vectorial properties of light
  • Which textbook is listed as a primary resource for this course?

  • Div Grad Curl and all that
  • Optics by Hecht (correct)
  • University Physics
  • Thomas' Calculus: Early Transcendental
  • Besides lectures, which of the following is a component of the contact hours for this course?

    <p>Small group tutorials (C)</p> Signup and view all the answers

    How many lectures are scheduled for this course?

    <p>14 (C)</p> Signup and view all the answers

    What kind of problems are being used for CA (Continuous Assessment)?

    <p>Mastering Physics problems (C)</p> Signup and view all the answers

    Which of the following lab experiments is related to interference and diffraction?

    <p>JF Lab Exp 14 (C)</p> Signup and view all the answers

    Where can optional course content be found?

    <p>Blackboard (A)</p> Signup and view all the answers

    What does the expression $\oint \vec{E} \cdot d\vec{A} = \frac{Q_{encl}}{\epsilon_0}$ represent?

    <p>Gauss' Law (C)</p> Signup and view all the answers

    The equation $\oint \vec{B} \cdot d\vec{A} = 0$ mathematically expresses what?

    <p>The absence of magnetic monopoles (D)</p> Signup and view all the answers

    What physical phenomenon is described by the equation $\oint \vec{E} \cdot d\vec{l} = - \frac{d\Phi_B}{dt}$?

    <p>Faraday's Law (C)</p> Signup and view all the answers

    In the context of Maxwell-Ampère's Law, what quantity is represented by the term $\epsilon_0 \frac{d\Phi_E}{dt}$?

    <p>The displacement current (C)</p> Signup and view all the answers

    What is the significance of a wavefront moving in the +x direction with velocity $c$?

    <p>It depicts the propagation of an electromagnetic disturbance, where points behind the front experience E and B fields. (D)</p> Signup and view all the answers

    Which phenomenon is NOT typically associated with the wave nature of light in physical optics?

    <p>Refraction (D)</p> Signup and view all the answers

    What distinguishes Fraunhofer diffraction from Fresnel diffraction?

    <p>The distance between the aperture and the observation point. (B)</p> Signup and view all the answers

    Which optical element is most closely associated with manipulating the polarization state of light?

    <p>Polarizer (B)</p> Signup and view all the answers

    What is a key characteristic of coherent light sources compared to incoherent light sources?

    <p>They produce light with a well-defined phase relationship. (C)</p> Signup and view all the answers

    Which mathematical tool is used to describe the polarization of light?

    <p>Stokes Parameters (A)</p> Signup and view all the answers

    What phenomenon is exploited in thin film interference?

    <p>Superposition of light waves reflected from different interfaces. (C)</p> Signup and view all the answers

    In the context of diffraction, what does 'resolution' refer to?

    <p>The ability to distinguish between closely spaced objects. (C)</p> Signup and view all the answers

    Which of the following is a characteristic of geometrical optics?

    <p>The size scale is much larger than the wavelength. (B)</p> Signup and view all the answers

    According to the derivation, what is the relationship between $E$ and $B$?

    <p>$E = cB$ (D)</p> Signup and view all the answers

    What physical constants are required to determine the speed of electromagnetic waves using the derived formula?

    <p>Both permeability of free space ($\mu_0$) and permittivity of free space ($\epsilon_0$) (B)</p> Signup and view all the answers

    Given the values $\mu_0 = 4\pi \times 10^{-7} \frac{Tm}{A}$ and $\epsilon_0 = 8.85 \times 10^{-12} \frac{F}{m}$, which calculation correctly determines the speed of light ($c$)?

    <p>$c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$ (D)</p> Signup and view all the answers

    What is the significance of the Maxwell-Ampere correction to Ampere's Law?

    <p>It introduces the concept of displacement current due to a changing electric field. (C)</p> Signup and view all the answers

    If a cubical surface is placed in a uniform electric field E with two faces perpendicular to E, what can be said about the net electric flux through the cube?

    <p>The total flux is zero. (B)</p> Signup and view all the answers

    If a disturbance exists in the electromagnetic field, what can be determined using Maxwell's equations and the provided derivation?

    <p>The speed at which the disturbance propagates. (C)</p> Signup and view all the answers

    Which of the following is NOT a direct consequence of Maxwell's equations?

    <p>Electric charge is quantized. (C)</p> Signup and view all the answers

    What would be observed if the Ampere-Maxwell law did not include the displacement current term?

    <p>Changing electric fields would not produce magnetic fields. (B)</p> Signup and view all the answers

    What is the result of replacing $x'$ with $x - vt$ in the equation $\psi = e^{-ax'^2}$?

    <p>The wave moves to the right with velocity $v$. (C)</p> Signup and view all the answers

    In the context of harmonic waves, why are sine and cosine functions considered important?

    <p>Any periodic signal can be described as a sum of sine and cosine functions using Fourier transform. (C)</p> Signup and view all the answers

    What are the units of $k$ if $kx'$ is in radians and $x'$ is in meters?

    <p>radians/meter (A)</p> Signup and view all the answers

    Given the equation $\psi(x, t) = A \sin[k(x - vt)]$, what does $A$ represent?

    <p>Amplitude (A)</p> Signup and view all the answers

    If $\phi = k(x - vt)$, what does $\phi$ represent?

    <p>Phase (angle) (B)</p> Signup and view all the answers

    What physical phenomenon is described by the statement “the ‘disturbance’, $\psi$ is the same at any position $x$ and the position $x + \lambda$”?

    <p>Wave periodicity (B)</p> Signup and view all the answers

    What is the relationship between the second partial derivative of $\psi$ with respect to $x$ and the second partial derivative of $\psi$ with respect to $t$ according to the wave equation?

    <p>$\frac{\partial^2 \psi}{\partial x^2} = \frac{1}{v^2} \frac{\partial^2 \psi}{\partial t^2}$ (A)</p> Signup and view all the answers

    Given $\psi(x, t) = A \sin[k(x - vt)]$, what happens to $\psi(x, t)$ if $x$ is replaced by $x + \lambda$, where $\lambda$ is the wavelength?

    <p>$\psi(x, t)$ remains the same. (B)</p> Signup and view all the answers

    What condition must be met for a sine wave to repeat every $\lambda$?

    <p>$k \lambda = 2\pi$ (A)</p> Signup and view all the answers

    How is the period $T$ related to wavelength $\lambda$ and wave velocity $v$?

    <p>$T = \frac{\lambda}{v}$ (D)</p> Signup and view all the answers

    What is the angular frequency $\omega$ in terms of frequency $f$?

    <p>$\omega = 2\pi f$ (A)</p> Signup and view all the answers

    If a wave has a phase shift, what does this imply about the wave's 'disturbance' at the origin?

    <p>The 'disturbance' is not necessarily zero at the origin. (B)</p> Signup and view all the answers

    Which of the following expressions represents a wave with a phase shift $\epsilon$?

    <p>$\psi(x, t) = A \cos(kx - \omega t + \epsilon)$ (C)</p> Signup and view all the answers

    What is the relationship between wavenumber $k$ and wavelength $\lambda$?

    <p>$k = \frac{2\pi}{\lambda}$ (B)</p> Signup and view all the answers

    Given $\psi = \sin(\phi - \frac{\pi}{4})$, how can this be interpreted?

    <p>A sine function shifted by $\frac{\pi}{4}$ (C)</p> Signup and view all the answers

    How is $\cos(\phi)$ related to a sine function?

    <p>$\cos(\phi) = \sin(\phi + \frac{\pi}{2})$ (C)</p> Signup and view all the answers

    Flashcards

    Electromagnetic Waves

    Waves that propagate through space and include light, radio, and X-rays, composed of oscillating electric and magnetic fields.

    Polarisation

    The orientation of oscillations in a light wave, which can be linear, circular, or elliptical.

    Interference

    The phenomenon that occurs when two or more waves overlap, resulting in a new wave pattern.

    Diffraction

    The bending of waves around obstacles or through openings, leading to the spreading of wave fronts.

    Signup and view all the flashcards

    Maxwell’s Equations

    A set of four fundamental equations that describe how electric and magnetic fields interact.

    Signup and view all the flashcards

    Phasors

    Complex numbers used to represent sinusoidal functions in terms of amplitude and phase.

    Signup and view all the flashcards

    Vector Fields

    A representation of a quantity that has a direction and magnitude at every point in space, used in physics.

    Signup and view all the flashcards

    Coherence

    A measure of the correlation between wave phases at different points in space or time, essential for interference patterns.

    Signup and view all the flashcards

    Electric Flux

    The amount of electric field passing through a surface area.

    Signup and view all the flashcards

    Gauss’ Law

    The electric flux through a closed surface equals the charge enclosed divided by the permittivity of free space.

    Signup and view all the flashcards

    Faraday’s Law

    The induced electromotive force in a circuit is equal to the rate of change of magnetic flux through that circuit.

    Signup and view all the flashcards

    Maxwell-Ampere’s Law

    The magnetic field circulation around a closed loop is related to the current encircled and electric displacement.

    Signup and view all the flashcards

    Wavefront Concept

    A surface representing points of a wave that are in the same phase of motion.

    Signup and view all the flashcards

    Linear Polarization

    Light waves oscillate in a single plane.

    Signup and view all the flashcards

    Coherence Length

    The distance over which a coherent light source maintains a defined phase relationship.

    Signup and view all the flashcards

    Apertures

    Openings that allow light to pass through, affecting light's behavior.

    Signup and view all the flashcards

    Fresnel Diffraction

    Near-field diffraction pattern created when light passes through an aperture.

    Signup and view all the flashcards

    Quantum Electrodynamics (QED)

    The quantum theory that combines quantum mechanics and electromagnetism.

    Signup and view all the flashcards

    Electromagnetic Wave Speed

    The speed at which electromagnetic disturbances travel, given by c = 1/sqrt(μ0ε0).

    Signup and view all the flashcards

    μ0

    The permeability of free space, a constant used in electromagnetism, μ0 = 4π × 10^-7 Tm/A.

    Signup and view all the flashcards

    ε0

    The permittivity of free space, a constant used in electromagnetism, ε0 = 8.85 × 10^-12 F/m.

    Signup and view all the flashcards

    Maxwell's Equations

    A set of four fundamental equations that describe how electric and magnetic fields interact and propagate.

    Signup and view all the flashcards

    Faraday's Law

    Indicates that a changing magnetic field induces an electric field, forming the basis for electromagnetic induction.

    Signup and view all the flashcards

    Maxwell-Ampere Law

    A modification of Ampere's Law which incorporates the displacement current, relating the magnetic field to electric current and displacement.

    Signup and view all the flashcards

    Electric Field Orientation

    Refers to the alignment of an electric field concerning an area, influencing electric flux through surfaces.

    Signup and view all the flashcards

    Wavenumber (k)

    The number of wavelengths per unit distance, defined as k = 2π/λ.

    Signup and view all the flashcards

    Wave Period (T)

    The time it takes for one complete cycle of a wave, given by T = λ/v.

    Signup and view all the flashcards

    Frequency (f)

    The number of wave cycles per unit time; related to period by f = 1/T.

    Signup and view all the flashcards

    Angular Frequency (ω)

    The rate of change of phase of a sinusoidal waveform, defined as ω = 2πf.

    Signup and view all the flashcards

    Wave Function (ψ)

    Describes the displacement of the wave, often represented as ψ(x, t) = A Sin[kx - ωt].

    Signup and view all the flashcards

    Phase Shift (ε)

    A shift in the wave's position along the x-axis, affecting where it starts.

    Signup and view all the flashcards

    Sine vs Cosine Waves

    Sine and cosine can represent the same wave with a phase shift; ψ can be A Cos(kx - ωt + ε).

    Signup and view all the flashcards

    Disturbance

    The variable ψ represents the disturbance in the wave at given x and t.

    Signup and view all the flashcards

    Wave Equation

    A mathematical equation that describes wave behavior.

    Signup and view all the flashcards

    Harmonic Waves

    Waves resulting from periodic disturbances, primarily sine or cosine.

    Signup and view all the flashcards

    k (wave number)

    Constant representing the angular frequency of a wave, measured in radians per meter.

    Signup and view all the flashcards

    Traveling Wave

    A wave that moves through space and time, described by functions of position and time.

    Signup and view all the flashcards

    Amplitude (A)

    The maximum extent of a wave's disturbance from its rest position.

    Signup and view all the flashcards

    Phase ( )

    A measure of the position of a point in time on a wave cycle.

    Signup and view all the flashcards

    Wavelength (\u03BB)

    The distance over which a wave's shape repeats.

    Signup and view all the flashcards

    Velocity (v)

    The speed at which the wave moves through a medium.

    Signup and view all the flashcards

    Study Notes

    Optics and Waves II: Module PYU22P20

    • Lecturer: David McCloskey, Ussher Assistant Professor for the Science of Energy and Energy Systems, Trinity College Dublin
    • Module code: PYU22P20
    • Contact hours: 14 lectures, 1 revision lecture, 1 test, 2 small group tutorials
    • Course objectives:
      • Connect electricity, magnetism, and light
      • Provide mathematical tools to describe light as a vector field
      • Explore light's vectorial properties (polarization, interference, diffraction)
      • Understand applications of electromagnetic waves in technology and daily life

    Course Structure

    • Textbooks:
      • Optics by Hecht, Addison Wesley, University Physics Chapters 32, 33, 35, 36
      • Thomas’ Calculus: Early Transcendental, 12th Edition, by George B. Thomas
      • Div Grad Curl and all that, H.M. Schey
    • Online content: Mastering Physics, Blackboard
    • Assessment: Coursework assignments (Mastering Physics problems), end-of-year exam (2 questions, paper II)
    • Related labs: Interference and diffraction, Michelson Interferometer, polarized light, Fourier analysis

    Topics

    • Electromagnetism and Scalar Waves: History, Maxwell's equations, wave equation, phasors, sources of light, coherence, and vector fields (divergence, curl)
    • Properties of Light 1: Polarization: Linear, Circular, Elliptical polarization, degree of polarization, phase retarders, optical activity, Jones Calculus, Stokes parameters, polarizers
    • Properties of Light 2: Interference: Superposition, coherence length, interferometers (Fabry-Perot), visibility, thin films, localized/non-localized multiple-beam interference
    • Properties of Light 3: Diffraction: Near-field, far-field, diffraction limit, resolution, apertures, Fresnel and Fraunhofer diffraction, image formation, spatial filtering
    • Maxwell's displacement current: Ampere's law and its correction to account for time-varying electric fields in the context of charging capacitors. Key to understanding how electric fields generate magnetic fields.

    Electromagnetic Spectrum

    • Charts cover wavelength, wavenumber, electron volts, and frequency ranges for various electromagnetic waves (radio, microwave, terahertz, infrared, visible, ultraviolet, x-ray, and gamma).
    • Explanations of various bands and their applications including radio, microwave, terahertz, infrared, visible light, and their various applications.

    Current Theories of Light

    • Distinguish between geometrical optics and physical optics (classical electromagnetism). 
    • Highlight the importance of quantum optics.

    Historical Development of Light Theories (brief summary)

    • Early concepts (Euclid's law of reflection, Snell's law of refraction, Grimaldi's study of diffraction, light's finite speed by Ole Römer)
    • Particle theories (Newtonian)
    • Wave theories (Young's interference experiments, Maxwell's equations, Einstein-Plank)

    Today's Objectives (examples)

    • Understand course structure and content
    • Review of Maxwell's equations in integral form
    • Maxwell-Ampere correction
    • Derive the speed of an electromagnetic disturbance

    Scalar and Vector Fields

    • Scalar field: A field that only has a magnitude at each point in space and time (e.g., temperature).
    • Vector field: A field that has both magnitude and direction at each point in space and time (e.g., wind velocity).
    • Definitions & representations used for both types of fields

    Electric and Magnetic Fields

    • Explain how charge particles and currents exert a force on each other through electric and magnetic fields.
    • Introduce the Lorentz Force Law: F = q(E+v×B)

    Light as a Wave

    • Explains the experimental evidence for light having wave-like properties through interference and diffraction experiments.
    • Review of the theoretical connections between electricity, magnetism and light, specifically how Maxwell's equations combine these disciplines.
    • Maxwell's laws derived in terms of integral equations and the differential equation for electro-magnetic radiation which shows light has a finite wave speed c
    • Explains the derivation for the speed of electro-magnetic radiation and how this applies to light.

    Maxwell's Equations

    • Integral form: Gauss's Law, Gauss's Law for Magnetism, Faraday's Law, Maxwell-Ampere's Law
    • Differential form:
      • ∇⋅E = ρ/ε₀
      • ∇⋅B = 0
      • ∇×E = -∂B/∂t
      • ∇×B = μ₀J + μ₀ε₀∂E/∂t
    • Important vector identities: curl(▽ × E), divergence(∇ · E), Laplacian(∇² E)
    • Discussion of the significance of Maxwell's Equations for understanding electromagnetic phenomena.
    • Derivation of waves from Maxwell's equations.

    Example Questions

    • Electromagnetic disturbances and light: Demonstrate that a disturbance in the electromagnetic field travels at the speed of light by using differential forms of Maxwell's equations.

    Today You Have Learned (examples)

    • Review of Maxwell's equations in integral and differential form.
    • Derived the Maxwell-Ampere correction.
    • Derived the speed of an electromagnetic disturbance.

    Section 2: The Differential Form of Maxwell's Equations

    • Introduce the differential form of Maxwell's equations.
    • Introduce and define ∇. (divergence), ∇× (curl), and ∇² (Laplacian)

    Waves

    • Definition: A disturbance or oscillation that travels through space and time, carrying energy and momentum.
    • Types (transverse, longitudinal, plane, spherical, cylindrical)
    • Wavefunction y: A function of position and time that describes the disturbance

    The Wave Equation

    • Derivation: Derive the wave equation from the wave's definition using the chain rule and differentiation.
    • General and Specific Solutions: Explain the general properties for a wave, and also give examples of solutions in the context of harmonic and travelling waves.
    • Wavenumber (k): How many cycles of sinusoidal waveform take place per unit distance (m⁻¹).
    • Angular frequency (ω): How many cycles of waveform take place per unit time (rad s⁻¹).

    Phase and Phasors

    • Phase: a phase shift to a wave means the location of a maximum of the wave.
    • Phasors: Representing plane waves as complex (rotating) vectors on an Argand diagram.

    Light Sources

    • Coherent light sources: Light sources with a fixed phase relationship, useful in interference experiments (examples include lasers)
    • Incoherent light sources: Light sources without fixed phase relationship (e.g., lightbulb, sunlight).
    • Spatial Coherence: The extent over which light keeps the same phase
    • Temporal Coherence: The extent over which light keeps the same energy distribution

    Energy, Power, and Momentum in Light

    • Energy Density: Energy per unit volume associated with electric (uE) and magnetic (uB) fields
    • Poynting vector: The direction that energy and power flow in an electro-magnetic wave calculated from the electric and magnetic field magnitudes and wave speed.
    • Irradiance (Intensity): Magnitude of the average Poynting vector and the magnitude of power flow per unit area.
    • Momentum: Light carries momentum which is related to the energy density.

    Devices Using Radiation

    • Crooks Radiometer
    • Solar Sails
    • Optical tweezers

    Example Questions (examples)

    • Satellite stabilization: Applying radiation pressure to counteract space debris.
    • Collisions: Calculate the potential momentum change and risk level.
    • Particle Collection: Calculating the velocity of particles collected by a laser beam in space.
    • Antennae: Estimating induced electric fields from radiating power sources and antennae.
    • Electric field verification: Show the electric field E=E0e^(i(kx-wt) satisfies the wave equation.

    Studying That Suits You

    Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

    Quiz Team

    Related Documents

    Optics and Waves II PDF

    Description

    Test your understanding of the Energy Systems course with questions about content, resources, and fundamental equations in the field. This quiz covers key concepts related to energy, circuits, and the principles of electricity and magnetism. Prepare to evaluate your knowledge on these essential topics.

    More Like This

    Wind-Electric Conversion Systems
    13 questions
    Geothermal Energy Systems Quiz
    32 questions
    Use Quizgecko on...
    Browser
    Browser